{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T07:57:16.457264", "start_time": "2016-03-02T07:57:16.443739" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "from scipy.stats import norm,uniform\n", "import matplotlib.pyplot as plt\n", "import seaborn as sbn\n", "import pandas as pd\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "np.random.seed(282629734)\n", "\n", "sbn.set_style('white')\n", "sbn.set_context('talk')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The Convergence Problem\n", "\n", "From the previous notebook, we know that using MH leads to a Markov Chain that we can use for inference. This is predicated on our chain converging to our stationary distribution (the posterior). Knowing when a chain has converged is a numerical issue and there are some important diagnostic tools we'll be using for assessing convergence.\n", "\n", "For having some data to play with, let's resurrect our simple example yet again:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T07:57:29.999531", "start_time": "2016-03-02T07:57:29.604589" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data = norm(10,3).rvs(10)\n", "sigma = 3 # Note this is the std of x\n", "mu_prior = 8\n", "sigma_prior = 1.5 # Note this is our prior on the std of mu\n", "\n", "plt.hist(data,bins=20)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T07:57:31.333126", "start_time": "2016-03-02T07:57:31.276280" } }, "outputs": [], "source": [ "# a fairly basic mh mcmc random walk sampler:\n", "def sampler(data, samples=4, mu_init=9, sigma= 1, proposal_width=3, \n", " mu_prior_mu=10, mu_prior_sd=1):\n", " mu_current = mu_init\n", " posterior = [mu_current]\n", " for i in range(samples):\n", " # suggest new position\n", " mu_proposal = norm(mu_current, proposal_width).rvs()\n", "\n", " # Compute likelihood by multiplying probabilities of each data point\n", " likelihood_current = norm(mu_current, sigma).pdf(data).prod()\n", " likelihood_proposal = norm(mu_proposal, sigma).pdf(data).prod()\n", " \n", " # Compute prior probability of current and proposed mu \n", " prior_current = norm(mu_prior_mu, mu_prior_sd).pdf(mu_current)\n", " prior_proposal = norm(mu_prior_mu, mu_prior_sd).pdf(mu_proposal)\n", " \n", " p_current = likelihood_current * prior_current\n", " p_proposal = likelihood_proposal * prior_proposal\n", " \n", " # Accept proposal?\n", " c = np.min((1,p_proposal / p_current))\n", " \n", " accept = np.random.rand() <= c\n", " \n", " if accept:\n", " # Update position\n", " mu_current = mu_proposal\n", " \n", " posterior.append(mu_current)\n", " \n", " return np.array(posterior)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T07:57:53.142940", "start_time": "2016-03-02T07:57:32.460321" } }, "outputs": [], "source": [ "chain = sampler(data,samples=5000,mu_init=9,sigma=sigma,proposal_width=2,\n", " mu_prior_mu=mu_prior,mu_prior_sd = sigma_prior)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T07:57:53.986854", "start_time": "2016-03-02T07:57:53.144613" } }, "outputs": [ { "data": { "image/png": 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JuiqhloD1xBccrWEspfpybGxNBVgTT7BdQURERLZZDWC8DGA4gPmqx44C0CrL8kbVYzKA4wTVjYgc4AgMb326fGfQVQg1O0EJXqrG1KGgGE6vY7uCiIiIbLOUA0OW5R0AIEmS+uGeABpzNm0A0ENIzahgqJvl8Wuj+48Ja73FUQPi8EwaK1LNwYnbdyPbFUREROSEm4xgDQC65zzWA5m5q6EQs/ZeQWDn0D2eQaJ4UOcQKZCRVaFvVxAREVGw3AQw1gEolSTpUNVjEoBV7qpEhSaGQ6OJCFxG1a0i1UpaBTKwiu0KIiIiMuQ4gCHLci2ADwE8JElSD0mSTgdwHYCxoipHhYFTSNzjeQu/rZUNuPrZWXiTSUA78LI1popfFESwh+0KIiIiMuN2UflfAigFsA3AuwB+J8vyXNe18kAhNP6IAAYzvOb0/P7mP0sxv2wfRr23XGyFQoxTwtxRr+hSQJ/ryLQriIiIyH+Wkni2k2V5CoADVP+uBPBDwXWiAsNlVKkQlO/LzU1I/MAbKyqAHBhsVxAREZEdbkdgkIc+Xb4D5z86BXM2VgRdFQo53un2j9MzXSijwLICkmY5MLytSvRlBTCCqwYRERFRWNgagUH+unXsIgDANc/PQdnokQHXxjvqzneB9PE8xWCGx3h6LTM7VYUS1BGBn2txho6aYPs1cf4NJiIiipJYj8Bg4zgiFN1/kEW81MOvUN4i9dKfZsoqGryrSBzYGM1CREREVAhiHcAgIiJ/ZU8hYa9bFJ5LIiIiIgYwKASivIyqoih46NPVeHzS2qCr0iFq57BQ2BiYQJSHOTCIiIiIGMAgAgCMX7odN748D9v22RvSPm9TJZ6buhGPT1qHjXvqPKqdOQYt/OM0F0EhvkWFeMwiRTm4S0REROQFBjByvDh9I658ZhZ21zQFXZWCoW6YT1i+I5A63DluMaat3YO73lxi63U7VddJXXNSdLUohNiRtI7nSpy4LqNKREREZEfBBDCsNv0emLAaCzfvw30fr/K0PtRJfUe7tinYIMAGm6Mo1J2KIp3shVsrG/DnD1dg3qZKV3Wziv2ccOL7QnYxnwgRERFRtoIJYNhVKCMw9tW3YGslVwJoZ7ePkEp3/l1cpB3AuG/8Krw2ezNufn2Bi5oZY9fGPzzXdvBsicIzSURERMQARkFLptI4+a8TMeKRySjbWx9YPdRBg+MH9wmsHoD9u5xpVWY9vQDGpNW7AAD7GlqdV4xCRVEUTF27x1bOFDvLixIB2aPTOIWEiIiIiAEMXYXQVlRP1wgq90SuqJ33lIUpJBQ/Hy3djp+8PA9nPzzZ8muidm2LUIjH7BWeSyIiIiIGMCgEwpRp3+7uUxZGYPiB8+P9oygK3ltUHnQ1IoFXpThcRpWIiIgIKAm6AmFVCG3FMA4YiNp5Vw/rLg7jCSVfrN9dh5tfX4BrzzgUvxhxeNDVoZhgEs/wGDpqgi/7KRs90pf9EBERRRVHYBCAYBvH6n0H3ki3ncRTNYUkJJ+mwM9hzGmd3V+NW4wNe+rxwITVvtcnzHgpisMcGEREREQxD2C4ae9F9V76+t21mF9mbbnOhOoog2wbR7ldngrJuO5w1KJwVdQ3m26j8F0KJUVRsGRrFeqbg13CWYv6iklwhBcRERFRvAMYbkSxq9GcTOHCx6bh6mdnY0V5tfkL2B52jXdFCw/fcmNRm/YwZs5mXPGvmfj+0zM1n0+q10oOUBTOJREREZHXCiaAUQhtv5rGzjuIM9fvtfXasJyeoN8nu7tP+jQC4+35W/Huwm2Wtg3Le2lE3lmLijrzUQtEXvv7F2sBAGt31eU99++Zm3DsvZ/j1VllPtcqg0ELIiIiomyxDmBwxK33Kutb8NN/z8M97y0X0tiO2jD7tA8BjBXl1fj9u8vwm/8sxbpdtdobRei0Ld6yD99+fBpOfWBS0FURJsHhTJoidFlqum/8KrQk07j3o5VBV4WIiIiIEPMAhpv+tKIoaEmm8c8v12H6uj3iKuUTvzoO7y3ahinyHoybtwWbKxoclZE95FxQxRyyG4TZUtl5zF7VfWd1U8ffe+tavNmJj96ctzXoKrgS9U65n4L+PBMRERFRvMQ6gOHWyzM34bGJa3HDS/OCrooldkecqLd32tGoaWzt+DuZdjZXPGqjLtSKi+yd9Mr6Ftz99hJMXLXL8musnB31ObT7XlbWt6CmqdV8Q0H8mnYTNEVRspK8hqUzX1nfgjU7a4KuRmiEeZpGiKtGREREFAgGMAwsKNsXdBU8JXrQu4jGdtDtdbv7L7IZNfrThyvw3qJy/PK1BTb3lCF6WlRFXTPOGv0lzn1kMhpbUmIL1+E00BUaFi70lmQalzwxHV//v0nYXFHvQ6WsSaUVfPvxafjO49MxY529PDlORDk4SUREREThE+sABhvP1gV5rqK2aoEby7dZWB3GR9PW7UFTaxr7GlqxYU9+EkMvyDt18nhEiFkgadPeeqzZWYu9dS34ZPlOAMEH5wCgoSWJPbWZ5KnvLy7Pe35rZQP+/OEKLNla5XfVLNla2YCfvDwPnyzfIazMMLwvRERERGRNrAMYbgWZBHTbPmf5JOxIqA7QadxAdONfq7wV5dW4/Y1FWLnd+85/GOMnVoI6WUEgG+9KEMkn+3Qr7fg7igErBfauk1RIR5xoXSf3jV+F12Zvxp3jFonaiVB3vLEIU9fuwW1jBdWPiIiIiCKlJOgKUL5kKo1Ln5gedDVsc9pXUXT/kXHZkzMAAJ8s34FND410uBdv2D1mtyNdRIcbAgnS5eReidpqQVaCF1rvcxQOc9LqTG6WrZWNQsoTHZ7SWurUjXRaQW1T0nzDgEQwvkcuDR01wdPyy0aH6zeUiIjILo7A0BFku7GxNYUal41qKw1fdYcqyONV34U3qkfYG/Ne1c+vw/br/Jpdd6kIJPnMDbpYCcKE4aiCqIOiKGhqFZNfxU4AcGd1Ex6csMowYelXa3aLqJYvwv79R0REROSHgglgOLnzHYU7pmpB1zcODeyo5k1R19r5dCDnx/7Fyp2Yt6nS0rZFWVOXsvf54ZJyHHfvZ/jrx6sc1yUM4vBZcCr3WrzhpXk48S9fCM1bYcVNry/AC9M34TuP649m08oDIlIylcbkNbs78o4QERERkTsFE8CIErt9n5ZkGi3JcM6zt6KA+3qBSwiYv7FkaxVuen0hfvjcbNQ1m48cylq+N+e5P32wAk2tabw0Y5PreoVF+zkOXVDDh/o0tqYwY/1etKTSeHrKeu93qLLMQsLctMdvyoszNuG/XpmP8/8+xdHroxpQJSIiIvIKAxgR15JM44LHpuCCx6agNWWvsZvOXv7DdV1ENLajPIrEj86GiICDHqfHvmhz53LDVQ0tpturDyG3A+l26pQf7Oa3CGuiUq9qlTVFSHXs9c3+LNNrh9fTldoDcbUWAntEREREZI5JPEPITn9n9saKjoR7szbstfy6PbXNOP/RKTZrlk9E3yx7BY14c5Ic0VLSSAvnsL0zqQ6CBJ0HJaR9e0Nadc59KKzH5Ue99Hbh9WgHJ4JMt7K7pgkKgIP6dNPdJoSnjIiIiChQsR6B4epuegRXR8gemm988I9PWpuVfT/YdnJ4WunhqYk2p9dkKq3g+0/PwvefnpV111nENW73nBVF7YPlktaomcp685EqcSAiN0u7TXvr0dQqdqpcUEGV2Rsq8I2HvsQ3HvoS09ftCaQORERERFEU6wBGZDlsUydsTMDIzZkheiSFU5v21qM5GeBQc5dBr7Cau7ECS7ZWYcnWKszdWKG5TWW9/4kGw3zO9DhdRlXtp/+el/XvFeXm+RrC5r7xK/HTf88zzL+jnkLiNlhw65iFrl6vJagAxoryaqSVzLW03OC9j+DHg4iIiMhTDGDYkEylQzufHbCXg0HUTXAReR9yT+n4pf6uVhAG7y/ehtvHLsI+zTvz5udY/T5oXaJJ1aiLVvUIDFXQ62evLEC9D3P11SMSwjitwAlrH6fOY81NMHnZkzOE1scKN99l1Q2t+PfMMkyR9+DdRdsslev2rS6rqHdXgAavc2DoXRdMzklERETkTMEEMP768SokU9aHH+c2L1fvqMGpD0zC95+ehXSQE6c94kUgwqmNe+rEFOQDUcf867eWYsLyHXhgwmrD7dQdomXbqjBtrbXh51nTi1SVzg1kbdrrrpNoJclo0Hk3vJDKuRBCG5cRVK8W1XdpdWOr/u6y8gR3/qOhJYmPl20XUpcvVu7Ei9M3OgrIBPU+Wd2v2TGl0woq6rhEKxERERWOWAcw1G2/MXO2YNy8LY7Lemv+VlQ3tmLJ1irsrGkSUDt9ToMJdqaQ2NnWa7lHG9UUCSL6QustBm8aW1L43lMzcePL87BsW5Xp9ur326iefnTo9IIpelZtr8l7rDWVxhtzt2Dl9nBMvdhV09mJtBMojYLyqkb8atzirFwN6u+oopzPq6LztzruO+rd5bjjjcWu69aSTOOm1xfigQmr8dmKnbZf7/UIDD2icoPc/sYinP7gJEy1GMgkIiIiirpYBzBybdhj/e5yAtmdvoaW8C+DF/Sw5KD3L4LWMazaXoOd1d4Graxqr11VY+dUk3mbKnM6QRrLfOoEhYKIFdkdgaEVeHxlZhn++P5yjPxnAFMvTJ7PHY0RVlZrefvYRfho6Xbc8JIqb4fqxXnBUJ3VmdXThT5aan/0hfbUqM5g0aod+YGudnpTo4KawuR0t4qiYHtV50pGn67YibQCPPLZGkE1IyIiIgq3WC+j6uZOfm770s+bqnYat7pzrE3KyD03Qfa5/Mi74NSK8uqO/AQb/+9SFOXebvaB1nuj7jTa7oSpO595fU/vLwT1NBOn193E1bsE1cY+82H9eq/zoDIm9tW34IaX52JQ3+547oZTs56rrG/B+KXbcZ40AL27leqWsWRr/ggf9aEYfc+qr00FwCfLd+BBk2lSTuWe36MO7IV1uzMjmpqTafTsalw/P+V+zh79QkaPLiW49bwjcrbLdt/4VXhlVhnu+95x+MlZQzser2nSn8ZDpDZ01ARXry8bPVJQTYiIiJyJdQDDLb2h7mG9vxrEtBA37f/mZAq/f2cZPlySfTc2yOktucfz8bLOhKKt6TS6FhXnvsL7Omk8VpR1bZqXkT3qwX2d99W3oG/3UhQVJWznHsiqi8MLSH386bTie2DJaG9hSkz6wZJyrCivwYryGpRXNaJX186v/Onr9mL6ur245vRDMPrKE22Va3SMeteXoii4bewiW/vJLjef0XdFvx76QZl2QaUzUp+++WWVmCJnpoBccvxADD2gp+7rXplVBgC496OVWQGMEF1yRERERJ6K9RQSkY06P4eF+7Gn/Dvv7tk9Ra/OKssLXgTN6BDMAit+rlCTvZKHhTn1ugGP7GOycgiLtuzDyX+diJ+/Ot9oN7pEjMBQj3JwMh3BLaNqpxUlNB3KhpbOJYn1Roa8OX+r7XLVx5ebuDUrcafqcdfBAhev1/tsWskf4zX19LTchKhOr6PqBo7IICIioniKdQDDlZyWo7rxHealVJ3KPaRkKo0V5dWerrhSvq9R8/EwJfE0H63gb2Xb36es0UEGdZy9oQIvz9ikm5fA6Fy3JLV7vPd+uBIAMFl2ljgwu+7OqAOK63eHa9WasC5SdO7fJ+N/P1ghpKysKSRG26lHroXwe7M15fEyqgF8l42Zsxkn3f8Fnpu6wf+dExEREXmsoAIYbhrQUVs69W+fy4bHa7bc5aj3luOyJ2fgwU+8ma9upQ5BsH+NBHNdFOWOYtCp97UvzMH9H6/COwu3dW5vUG77c3/+cAWG3/8FVpRX477xK/GXj1Z2fAZEztYQ0akN4jIy67TnBpUWbt6HivoWnVf4Q1Gyp0S5K6vz+KyO5vLiK9Tqe6+166bWlMaj/rB+3VvbTl1ce5DqoU+Z2JOIiIjip6ACGG74udyeqDuVe2qbdZ/LbffndrjaO7wvzdhkuI9ohXUcsHGATs+F2bKb2kk81c9nb6BVj7mbKjW31+v/vTZ7MxpaUrjsyRn498wyvDKrDAs27wOArHwTjS32O4HqfUYsLgjAfFh/7jElEplAkl1NrSl8uKQc5VXaI5WClDWKx+A5vVVIvLBxb11WoNlsytfzHBrWAAAgAElEQVS+Bv8DSoqiYP3uOiR1LnwrwUUiIiKiQhbrAIbbZIXqu3tZ2fQDbEnurWvGM1M2YNu+BgD27j6v312LHdXedYZEnRevb6grioLb31iE616Yoxs8WL+7DlPXZk+R8GqFjrFz85cJNZN9bdp7bfYKErn5C/QLq2vOzKtXrxozdu5mezuH9ekv1ssLIHmtwXO5OTAURX86jpGXZmzCXW8uwW1jFtqvoMeMcmCs3F7duV3W3CWX+zQp4JPlO/Hbd5ZaKiudVjB5jbMpUG68NGMTLnxsKh6ftM73fRMRERHFQawDGG5VqRKh+bmygNGefvHqAjz82Rpc8a9ZmW2N8hmo/r1pbz0ufGwaznzoKzQnU6HKM+G3jXvrMWHZDszaUIHPV2ovx3nhY1Pxk5fnYcb6vZ7XZ/aGCsvbtgcY1HeXFcVe39Dppdz+OvXrnQzDLxKRBEPF70vZrCNd35zEyzONRy5Z8fTk9QCApduqTbb0n/oc5E4pGtC7c71SkSMwrLz8vUXlmo/PV41AAoD3Fpfjj+8vd1UfJx6wuYRsCNOGEBEREQWKAQwdCoBZqo6ln1NIjCzZmsmav7dOf3qIli9Xd3bU99VrZKh32al1QjeI4nF0pVU16qIxpwOeezgrt9d0PmdyrI4DAyYnX/N5g1EM5lOQ9KeQGA5hb3tSHYBwMvpBRPxCvdew5cB4c/7WrNV1nNZPnah05vq9eGbKhkDzNqhlfR0aHGB2AMO7+mhSVevWnOVb315gf+UVrzBIQURERGRdSdAV8JObdqJe4/vDJeVYvq0af7hkGEqLxcSD7DRo1XcR7bzObH64E3anA3hRh3a7a5rQkkpjyH49DLfLyx8Rwc6ElY6h1bwqRpu1PyUyYJA91cLZyffyOtJiVs3dNfaCi1ru/XAFmlo7A23XvzgXANCzazFuPHOo6/LdMsqjoreMqhdTsAzfC4PnojIAzXKqzyh+cRERERE5wBEYFukNf77rzSV4ccYmjJljPxeAW5X1LdimsxQpoN+x0+pIxKn529iSwhn/9yXOfngydlY35T0vssMbin5DTs4FC5t3sBOMaO8kFRssQ2KlPPX5N8otc9NrC3RzRwR52s32LSLA8+ps7e+T6eu8n9JkhcUBGFlCMogNgH+jdvwKroXo1BIRERF5qqBGYLhhNoVk7a46n2rSKTcBpZ1GuRcNeLudeb06uK3alsqGjr+nrduDH552iMsSrRKQkNLBHnIvTbNapA0DGPqvFjUCQ28KSe6ev1i1CzMt5CApSmSmBVU1tGblX/CK2d3uUAS12nh1Z37D7s7vu2LDKSSK5t9O2H61wXWqF1iYvGY3XpqxCTefezhGHDXA7h4dkXfV6j4XpmuJCACGjpoQdBV8VTZ6ZNBVICKiHByBYZGfq5CIGmqtHyDIfyJOQ5BLizuPb0FZJVbvqNHd1m3ySxGBILe5NexeL06vL0XJBPJWlHeeTyfHr86bob7utEY55eYo0S4PuPKZWTj9wUlYtq3KfoVsMsv7YfX8zi+rRIXNXDZhmfrQrBoZc2j/7GlaWUEpRftvJ7S+o5xey3pv4X+9Mh8z1u/FneMWOyrXSzH6iiYiIiJyLNYBjNwGn5sGoPnw52i1LotyWvBeJaB0wm1QQJ2L5O0F23DJE9NR3aiRuNQmzak3IXjbU2l7AaisKSSwcx0o+HjZ9qxHcl+/bFt11jKrWtSvMFulwsphJRIJLGtbqeORz2TzF9igKIrp8eTVx2KY4epnZ3fktvCKL0vMWtxFMkRzSMxOi3oFqigIw/cQERERkR9iHcBwI69B6GcDMYAVQUQcnt0yvOpadSnJv6y37WvQ2FJsHYLqROQGVqoaWvOTk+q9OOcEmK1CUlHXovl4u5tfX4ifvTLfoJRsd7+9BIu37Msrx6kZ6/eioq4Zi7bsEzKq6O63l+Kk+77AxFWdq/iIHK20Zqf+9IEw0zoDu2qa8kaUeBHgtMros+134lengjx/RERERGHEAIYDStud6GufnxN0VQw5baJ/vnKn0Hro8ermsJ1i3U4hEcH6oqeqOpgMzX9x+iZH+zNbhSQ3f6fWezh3U6XBHrLLmF+2D99/epbpvu04/cFJ+MHTs7KCDk69v7gcybSC0Z+u1t0mbWFkgVHiUy/5MjVMAXbXNmHEI5Nx3t+nZI1Y8Xy6ncPyg1h61wqv3q/npm7ATa8tQGNLOJbhJSIiInLKdQBDkqQLJElaLElSrSRJsyVJ+rqIioXd/eNXYfbGCt3nF5RV4skv16HJwhz+XH7cc8ttwOfeRXdCVOPbkyVeHa68EYRUWsG8TZVoaLE2dSGdzr9P++Anq7GivLrj33rLldoK9ijaUxLsnk+9aQ2aU0h0Pg3qY8idDtUeTxg7d4u9ihnYZzCl4P3F5aavDyh+4ZvZGyrQkkyjtimJTXvrOx4X+V2WW1ZVQwsaYt4ht/qVajZS46FP1+CLVbvw3LQNAmrlvUJtVxAREZE5VwEMSZKGAvgIwNMA9gPwAIBPJEka6L5q4VbTZDxH+qpnZ+PRiWsx7E+foTkZ/ka246HKJi97+LM1+Pkr8zXPgS/z8wWyM1LCjae+Wo8fPjcb176QyY9gFhiqamzF0q35ySsve3KG6b5y3wOjfSlQNIMVtlef0S3fOifLeIqSW8/1e7JXIMqtTwIJYdf6F6t2obI+fxqPHtGfsW37GnDPe8vzRmnpXQPrBK7OlLuP4fdPxOkPTnJUll/fPerdtKa0lwT2k9ay0mFTyO0KIiIiMud2BMYlAJbLsvyCLMtJWZYnAJgL4Gr3VXNmQVkl7npzMTZX1Jtv7JDdDtsHFu7QekGvkb65oj4vMaGIwRO5w5ObWlN4ZsoGfLlmN8bZuBtutW+hKApWbq+21DHQPb4QTDHPrds/Jq0FAM2ghJZ3Fm7DB0u2m2+osz83HHUDdV6kNQLDszp4SOswRI7AeH7aRht1EXuBj/50DcbN24IJy3Z07iNnG/Wh9unOlbrbjXh4su3XWB6BEYLvMYFC164gIiKi8HDbuiwGkJsdMQ3gKJflOvbs1I2YtHoXBvfr7qockcnT7A5zFrkiiKIoqM0JVvzIo9wd1+WsqKDukFZqDMF326d76qv1eHTiWlx07EF44cbTOh7XOn3qc+N0v5rLOEak46A+fqNzYZYfI3d7R8uo6rwDisMb1H7cTHcbCMid5uLG+t3iRjXYpZffxKtkk7PW78VjE9finkuH2X6t0SkPIui1syb8ox9CInTtCiIiIgoPtwGMzwE8LEnS1QA+AHABgPMBWL8dLFhL29345mR+b8hNI3temXFiQiNBdXITAG4ZsxCTVu/G8YP7Gm7rtINm+VW5q2IIOCmPTsyMVGhP1qgoCuaX7XO8HGcUiOgoGibqNEnimTuqx0m+Er2OZZRWXFCfBytnQGQAI0hWjuLLNbs7/nb7uWsPil75zGx3BeVIhWhJV8oTunYFERERhYerKSSyLK8D8EMA/wtgB4DrAIwFYG3su4cUxd3sgBXlNfplI79hLrKDLLIj9/nKXUilFdPpCEZ71FuC1Iy6c6su//U5m3H6g19ivk5QyGlXb+b6Cvzwudm4xqMRJqY5MAS8bXbyG9iRncTTaRnaOTDs0ivCaZ/Sp4U2cvbZ+cg6CyMigopfiMj1YFaEoui/B0GGCeZs1A869+tR6mNNnLP6WxCncEyY2xVEREQUPFcjMCRJ6g1giyzLJ6kemwPgCbcVc8qvfoLThINectORM3rtlsoGDNmvh+0y9To+f/pgBQBgb12z7TKNTJF3m28kSGsqjdJi8asQb6l0Fiyyw3CaiMnVqjXiwm7ATe+6sJMDI9ARNTn7trJca1AjMESMdIrL6CW1riXFQVdBqDi9R2FsV1DhGjpqgm/7Khs90rd9ERFFmdspJPsDmC1J0jkAVgD4BYBDkckgHqjmZArl+xqDrgYA+50IUY1RUX2mtIDk+XaOaVdtE779j2n4zvED8euLjra+DwfP6eUN0dy27eG/fb4GL88ow+s/P8Ny3bTLU/Db/yzDpNXmHeC81woKi9kKxGlsnEjYv171OvNa5YS1Y2Z3ZIPIJJ5Bzkaxve+QvoFRma6UNXIqInUWILTtCiIiIgqe2ykkZQBuAfAugL3IDPu8SJZl75YAMdHewB47dwvKq7IDGKLa0qIz+4eBUeM4KSKCYcOYOVsg76rFE1+uw7pdtZZfZ5zbQZW40mUH8F+TN6CxNYVfvrYgex82OxirdtTg3UXbTLfLOi4Bl57h9Wv4lPYUErtTP3RzYNgZgWFvl4FKJIIbgSF6CondETihfZ98qlg8Mp/4K4ztCiIiIgoP12vcybI8BsAYAXXxnNGUhbcXbMU+O/kHQtgy92oKidPlLUW49oW55htZIOQIcgpp0UgUa4dWolk/OIxfaK5C8sCE1SKqBMBFDgxhNRBDq0N/4pC+mCzvCaA2YukHn/ythxMtyTT+5/3lqGtO4tMVO4OujibnpzECb4ANUWpXEBERkb/ET+IPsc9X7sJTX63Le3xPbTN+/84yPPTpGsdlW0nkZ5VWU3TbvgZc+sT0rMc27BF3Q8qo+ZtMGdxh9bjnYidPhuGdYA+qqZjs04yfd2ezB3GollTNWx3GoAxF1EgC7TJkjdE2j3y+Jm8kVRCyh/Ib0xqlMPSAnrrbLzFJsOuG6M9nlGeQvDa7DP9ZuM1y8OLWMQs1H5+2dg+uf3EOFm3ZJ7B27oTpPBMRERF5KXYBDLMG9t+/WJv3WFWDvZUftNqKCzfvQ9le7YCCiMbl2Q9Pxqod2SujXPuCuNU2FAVYs7MG12mU+acPVzgqs6yi83wEP39bQDJDGHf27b7PIob3W6XuyBqPwDCZDmCxynM2VuC8v03G+KX5Kx/qHXYylT8iZWtlI75ao5Gc1cLxiDy96rqJDgpc8a+ZtrZPIDOa4OevzMdDn4gbAWNp33r5S3S2D/5z38lugly9QMftYxdh5voK/P6dZSKqRUREREQ2xC6A4YTToeu5pq4VM0TcaQcpf6lHe69+fOI6zNpQkffMrppm7K5twrJtVbbq9uu3luY9ptVJFcXJabOTODIvYOGyc2a1f501YsLhvvbWaQfp7FwziqJg0WZrd52veX4OyioacOe4xXnP6SW0FH0XWWR59S0pV68XfWxvLdiKL9fsxnPTNqKuOam7nR9BsswyquEJVHittu18rxc46k6P6NMaZAJYIiIiIhFc58AIGycN9pSDCIZW51UvV0SY7kLqURQYDtW/+fWFWLylCteecQhakgp+dvZQHDeor2EDe09t/vSPW8cuElFdl8S04t12LqxeqsI79g6fm7l+Lz5Ykj+iwi6tKRZ+Kttbjw+XbMePTj8EA/t2C7QuTlWp8vWkPJ7ilYDzwFkBxTWEa02l8dHSckvbWj3NfD+IiIgo6mIXwHDCbpJKvc314iB2G41OG5luuoVNrSnDQM7iLZl5+uPmbQUArNxejc/++xyTUvPLm7jK/pKhIohouOeNVnC5j6BWprC6WksuEcELQPyqNnoBQr3T+/t3lmFeWSXkXTV4+vpThdbFL+pj8zpAqi49ynfwo9Z5f2bKBrwwfVPQ1SAiIiIKldgFMJy0r52MwNCi1/nzq91s1sE2Yrdzuman+fKmWYkPBZ2EyvoWzNlYgfOHHaixP/vLObqqVoAdIlcrzqgrnjctxlutqXRHEEzt9AcnaY7Y0WOlnnrnaF5ZJQDgk+WZHAcLN1diS2UDrhg+WMiUi9yAgug+fyKRPdLMz4651ukx2n174LNQubmexs3bYnnbQprCQ0RERIUtdgEMJzbutT+XWau9GORyo4DWihLe18doDxWqYe6iavKDp2eirKIB155xiK3XKUqm81zXpJ8vwLyM/KPw+y0XMpLE6RwSAbbqJFK0E7ywauraPXhx+kYcMaAXNu6tx8++OTSvQ6koCq58ZjYAoHfXUlx47EHC6+E1o7dMSEBGtQO96T/bq5o0H5+9MT+njp50WkGRXoIUAaIwlU9NVGBdLcojaIiIiIiAGAYwnDTQ7v1wpc1XaDeFFQX4bMVOvDU/+85ZKq1g/NLtGH5IPxzSv4f9CjrkQfs3cGUVmQ6w1l18I4qi4OpnZ2Pl9mr840fDOx7XulwszyfPXZXEZgfJ6hQSP3NgpBUFLUnvEq36fU0+MKFzlY6Bfbph5IkHZz2vPrdzN1VYCmA4OQThy5mqp5AYjTzycL9q/5iUv7qTXfe8txwPX3Wi63LiwouAOAdqEIXX0FETgq4COVQ2emTQVSAqKFyFBECNi7vyamkFuGXMQkyWs1cjeWH6Rtw5bjFGPDJZyH6sCtMdRz8azmYDC5ZsrUJrSsFLMzZlPe60fEVxd0czsLuh6iVIc46qNaXg7reXeLZrUZ0yJ8UsK8+fzuDJZenDta4eCeHnp1wz4CfoPX1rgb2gZNzprRykJTzf9ERERETeit0IDCczzkeecDAmLN9heXv9JJ7aT1Q1tNqqj6jOfiHdbWtNpbF6R43u8+pz0dQqZoSBAuNz/PiktWg2GM0QVADD6LK4ZcxCT/ctKoBx6mH7YXl5NQDgoN4WVxIx2bWwz52YYnQlkMi6doKeuhYVfp6mFeXVeOqr9YYrO4nES4CIiIgKRQwDGPYNPcD+tI4oJE3zo4ph6TzdPnYR5pft031ePdIg7XAeQ+6h5ucc6fx77a5aPD5pnWF5VpcTVbL+dn++nR6/CJ8ssx4oNHLUQb06/u7VzfnXmJI1GsXqa+yHSUWf8aAG74jIqREUP6/6y56c4er1Xv2+RPjtIyIiIgLAKSSB27inDrVNnSM0WlNptDpcZjK3yetHcCEk8Qt8YWN51pS60+pqNQ99++qtD/828/EyMcuXtkumxRy/VSvaRkqU7a3HP79aL7x8r95Dp6/zI7iZ1RFt211Ta8r7/Wo85mXOlELTfuk8NjE/p4jnCXyJiIiIIiB2AQw/7jCJagMuKKvE+Y9OxTdHfwUAaE6mcMGjU3HRY1OFlO9HW7VrqbVLKOh8HOqGu9PATl7SToNirAxysHpOpuTkVHEr6fMIjKfaghYVAoM6onix1G9uMV58J6kTwKYV4P3F23DcvZ/j1jEL8fSU9WhqTWFHdSO+WrNb7I41juWm172ddlRIrnxmFrZWNuBJm4G+KIwIJCIiIhKBU0gC9O9ZZQAySUSf/HIdpq3bgy06y0w6wUZtp6wAhkkH3s5509sy6ICNkWQqqDvm4s5J9ltkrVzNlYMc1EmBYjiFI3+qkdg737kBEQUKfv3WUgDApyt24tMVO9GjtBh/Gb9K3E7b9y28RP9E5evwTx+u0Hz8lbbfCyNmI784hYSIiIiiLnYBDCftMycNW62X2G4cqgp5VGPIsFu+NNitrzkaKPWoi5TTE+NmyRJBKupacNFjU3H84L6Oy2hN+TuFpLE1henr9uAJk5wgTrk5hsv+2ZmrYOzczbj53MNxUB/zpKBmK974Sev4p6wVO2qnXZRzYESFmxFXczdVCqwJERERUfjEbgqJE3Y7HKG9k5dTL19yYHi+BzHU9XSYYkRz6sWumibT/Yn06EQZ63bX4f3F5Y7LSDo9AQ5NXbsHN7w0Dws26ydZdcPNuV63u67j7+ZkGne8sch9fXI+d15PIdE6fiezhKyMPGL4Ipz0UtG+MnNT7qZEREREkRa7AEaQNwitrirRTvQ0g/qWZHb5HkcXPlux09sdCKQO5qj/tvMenDX6K5Ttrc96bPq6vab702Pl/fliZfY5trskrxa/c2B4TeR1brSSjZrhFBLNx8Sec/X3nFbgwcn0sZhdFoVF5737y/hVGDpqgr91ISIiIvJQ7AIYfgnjKIz7cua8e13FW8YstNxRCvp07azuHCnhZmTKPIMh2l4khHzo0zVZ/04J6GUmU3r3a6NpX4O15KCicsKYFuPDSc1ahETQ/qxcW9GeQeLuRC3fVo1LnpguqC5i1TYn8d6ibUFXg4iIiMhzMcyB4X0L2+3d1OZkCjuqtKceiFRIy6iauee95R1/m+WwNM5vYO2AvTr3DS3ul8qc5lF+BD+pz25zyJbx9COBa3Vj0vB5J9dfq8YH4573lmX924/vV7feWbgNT3wpfhnSez9agdU7atwV4qG7316KZ398StDVICIqOBzplq9s9Migq0AxFrsAhhOi+ppbKutNtymvauxYNtVrYWpsh2lFFDfBBasDIKxsZqUaXnQX9wmYhhImlkcB+XQJaqUYEb0KyT8mdXbQtcp2sj95V23eY+Pmbc3bd9j99j9LPSl3ydYqT8oVKURfs0RERESe4BQSiLtjmtvY1/LUV+uF7MuKO95Y7Pk+othebnQxisGog6C+joRNVxBSSrbuXTo/9mEKLDllNSCVVoCPlm63XG6VztQUs919ttLf3DBax+/kbbUyhaQlZKNd/FRSHP6fy+h/momIiIiMxW4Ehh93CN30+SLQBrYliv3fxtbOAIbd+lvuLBduP893ZlOC2r01fwtetrgqQ1VDC4bfP9FFrTotL6/BeBuBE7u0VyGx/8G08pKaJuOpK6LM2ViBijpruU2scvtdVVqUgNgaEREREZFdsQtgOOJjJ7woCmOwPfDlmt2WV3gIM6uXyort1UL2V5hXiz1WO+v1NkbefLVmt9Pq5PEyeAEASzWmNnj1lVbk8QVZ29SKT1fsxO/fWWa+sc+KTQ4+nVZQVJTA1BjkmCEiIiIKq9gFMAo0PhCYlpS1TuHGPeb5QcLCcJqIwZPtT22vasTjk9aZ78dCN9OLjmhVQyvufnsJLj72ICRi8IGJwzQYO3ITaf73W0vyN3JwSqycR68vlx8+NydUuXvUSg2Gz41fuh1/fH85fnuxhHs/WuljrYiIiIgKS8wmNPjDTX8pbn2tMXO2BF0FV+y+HWkLeQK07oiHSW1TEu8tKsctYxYFXRXnVB8kASvLxo5Xq+B4PYLMy+CF21xHRiMw7hy3GLVNycCDF1/4nH+FiIiIyG/xG4FhY9B9Q0sS/1mwDc9N2+hhjShOrHSBRI5q8Hp8RBQDap+t2JEVtPCis272FoZ94IqjHBgWtinUKXCA8QiMsPhgifF0pSiNhCMiIiLSEv4WmYeenbLB9ztmBdz+j4W0ApQWa7+J7R1AvsfeumXMIry/uLzj31ZGxYjUnEyFPvAjonrVGsvtRvnadvueleh87qNk7qZKzNtUGXQ1iIiIiByLXwDDRhvz2anORl64GYoc9o4PZTqoehRFMR3lY/UStHIteH25vL94m8d78MYS1TSdpM8BjCqNjr2vLFxgIk7JT1+Zl/dYFEYheMUsiWdUbNxTF3QViIiIiBwr3NYonAciuERmvBl1UK0EHUROIfEql0G7z1fu8rR8Pzw9ZYPwMo2CVJGIQQpYRnXxlvxcLl1LCvcnIx7hCyIiIqJoi11r1E4j02nf8JYxC529EO4TyZH3jK6LtKLoXmTtqziI7Oh4HcAg+9KKEvqpFF4NSony5ei26lr5Pz5cUo5t+xpcluyvsF+7REREREZil8TTD+VVjUFXgUTR6JEZBZmsJfG0tmsrwQmO9gkfRQl/R355ebXt11hb1jfkB+4hrc/1XW8uQbfSYO4DhH21IyIiKlxDR00IugqhVDZ6ZNBViIXYjcCwI4g7UVzyMfxMR2DoGDNnC6obWy1fVw98vNp0G47ACEaY71JvCnAliSh/f72z0F2+F70VWJpag4ky/uHdZY5eZ2elLiIiIqKwid0IDDv5B4LoG74xd4v/OyVbjC4LgxkkeHdRpoN02YkHW9rPvDLz1QB2VDdZKov8FWSAY9WOGm8KtvB9uH43E0CGxZqdtUFXgYiIiMh3BT0Cg0iL0agHxSTq9e6ibcz2R5Hzq3GLGSwzoTcCI3JichhERERUmOI3AiPoClDkXfDoVN3nPliy3fTuO69BipqPlm7H4q37gq5GqMUlfkFEREQUZRyBQQXN7iwiK0PoRS6jSuSXrZVMTmwkLh/rmBwGERERFajYBTDi0sik6OIlGH1mQah9Da0+1YTCIi5TSBhgJSIioiiLXQCDyGvM4h9/ZrlOFm7mdItCw089ERERUfBiF8Cw0sjcsIeZ9CnDi5VoIrzSJBHpiMvIhXgcBRERERWq2AUwrHhr/tagq0ARpjBEEXtx6aySOI0tqaCrQERERFTwYhfAsNLxaGplQ5Sy2emvejFqg4jCTd5VG3QVhGBsjoiIiKIsdsuoWtHeAWU/lNolIO56MMufQEREREREwSsbPTLoKpBNsRuBYQWnAFAuO1MGmpNpD2tCYcCb1BRXHIFBREREURa7AIaVtln7DXK244ijJYiokHAVJSIiIoqy2AUwrEhzCgkRERERERFRpMQvgGHp5hJDF5SN9yRJjcPsKa54bRMREVGUxS+AYQFnDVAukY16Xl5ERERERETixS6AYWV+LwMY5KX/+vd8YWWNOOoAYWWRdcwTQEREREQUPrELYFjBVUhITVEUdliJiIiIiIhCriToCohmZSoAR2BQu89X7sJTkzegJcWlUYko/uwsGU1EREQUNq4DGJIknQXgnwCOBrADwH2yLL/htlwvpRnAoDazN1YEXQVD7GwEg6edKDhRbFcQERGRP1xNIZEkqRjABwBGy7LcB8AvALwqSdJQAXXzDKeQEJERjtKiuAp7bC6q7QoiIiLyh9sRGP0ADABQIklSAkAaQAuAlNuKOcVVVClOwt7ZIKJoicDootC1K4iIKL6GjpoQdBUiq2z0yED262oEhizLFQCeBjAOQCuA6QDukGV5q4C6eaY9fqHwNiuFXAQ6G7HE804UjKi2K4iIiMgfbqeQFAFoAHA1gB4AvgvgcUmSThJQN0esJfFk4MKKK4YPCroKREQkUNhXXApju4KIiIjCw+0yqj8A8HVZlt+RZblFluUJACYAuNF91bzTHr5ggkRjI44aEHQVCt6q7TVBV4GIyHU6AkgAACAASURBVE+RbFcQERGRP9zmwDgUQNecx1rb/guElbtL7auQcCSGMcZ3glfXnAy6CgXnuhfmYNaGcK9OQ+RUBL7XQ9euICIiovBwG8CYCOAhSZL+C8ArAM4B8H0A57ss11Pjl27HeUdzdAER5WPwgihQkWxXEBERkT/cJvFcDuAqAHcBqAbwLwA/kWV5gYC6OWL17tLbC5gPzEwE7tQREZENYf9aD2O7goiIiMLD7QgMyLI8HsB4AXXx1dxNlUFXIfTCnuytEPAdICKRohCYjmq7goiIiLznNoln6EShcRYVPJdEREREREQUFrELYMTNnecfGXQViIgoNhiZJiIiouhiACPk2NQsbFzql4iIiIiIKMN1DozwiVmHL8AOLDvPweM7QEQi8WudiIgonMpGjwy6CpHAERghF2Rbk+1cIiIiIiIiCovYBTDidncpbsdDRETB4U8KERERRVnsAhhxE+RSpkWMnkRaEd8+IiIiIiKKkdgFMOLWZ2MMocC5eP/vv/x4cfUgUunfs0vQVSAiIiKiAhS7AEbcBJoDg8GTSOvdrQRdSvgRJ/HevfWsoKtADpXyO4GIiIgiLHYtmbh1uuN2POQzJegKUBx1jVEn+DvHDQy6Cr7q34OjZ4iIiCi64tMKjakglzJl7ISItAzs0y3oKghz1pH7B10FXzEoTkRERFHGAAbpYkOXiHL16FKMohhliI3PkVgTZGJoIiIiIrdiF8CIW+OsS3GQb1G8zmUU8R2gsOnZtSToKojFSC0RERFRZMQugBE3JcVsXBNReFTUNQddBaEK7RuW8RoiIiKKstgFMPxsnJ0/7EDP9xFkW7OUwZNICzJ/CsXXqEuGBV2FghOjGTtERERErsRsLLC/4t6o7NW1BMce3AerdtQEXRUiCokeXfz52XjhxtPwy9cWeL6fKMT5ihIJpBUxSwpF4XiJiIjsKBs9MugqkI/iNwIj6ArESCKRwP9edkzQ1ShobkdRKFxHlQTzqwN8wuC+vuwnCnmTigSe9CgcLxEREZGe2AUwou6AXl2z/h30NAA2dolIza/vBL+msEVhRILIOkbheImIiIj0xC6AEXSH360wVT+RCFd9yFz30uKOvxNgAIrE8+s7obTEn5+nKHxChI7AiMIBExEREemIXQAjboJubLKtGy3JdDrr35xCUpi+c9xAz8r26zvBryWkg/6OtUJkviUGNYmIiCjKGMAIGXXT8oyh/QOrB9B2Bz8KrfsYs3v6W1MMWBBwx/lHelY2vxL8xxEYRERERBmxC2DUNiWDroIw+/fq4vpe2aH9e7h6PRu7RNHTp1upZ2X7dQdfZKc96oTmwBBXFBEREZHvYhfAeHfRNh/3Jr4pqG6oFrkcN3zF8EH47kkHu6oLG7tElMWnLwW/4hdRmFLh9rdAjXEhIiIiirLYBTDipMhlFs1EIuG6cc7GbnQlEoDCGSUFycvPrV9fCQlkgrAkejQKv9SJiIgouhjACBl1wEFk4jZnEmBjlyia/nXdKZ6U61denKJEAo9fczJ+etZQb3cUga84oUk8I3C8RERERHoYwAix4oT7wc1uG6ts7EYb37/C1KdbKQ7u182Tsn0bgdG2o64eL6daWpzAVacOwbCBvT3djxsig0b8SiAiIqIoKwm6ApRN3U7t37OL+/Jc1sWvpQyjpnfXEtQ2hz9hLKeQFKZuXbz73PqWm6J9Rz7s7+9XnwQAGDpqgvc7c0DoBBJGNYmIKOTKRo8MugoUYuydhtidFxzlqrPgevQGgGMP7uOylHi65oxDgq6CqSgkJyRvFAkYvUXhIXQZVWElEREREfmPAYyQUTcu+3b3bilEq0Rmv48Tv+5icgSFOwf16Rp0FQLh5RKkft/AZyhG8DKqPJ1EREQUYQxgxJ3LVUxIm1+nRmEEw5U/XnpM0FUIhJeXp98BhTB/DXUvLQ66CrYxIERERERRxgBGiBQl8oMGrpdBdfVq0uNXJ4DhC3e8HIkQZp4uoxqzU+rms9ynuz9ppMTmwBBYGBEREZHPGMAIEeGdLbcrkIipRSz51glgBMOV4gKdApVIJGIzgirMR8HRDERERET+YgDDhcZWsatQaAUwuAxqYXMTv+B7X5gjMLyO2cQlMCKCX/Exocuo8u0jIiKiCGMAw4WZ6yuEllfkwbvh5g4hG7r6onJjv9AHcETlfRLJ6wCD36c0zN9DUQzmRLHORERERO0YwAiRBBJ5jXU2NcPJtxwYTOLpSiGPwPDqyON2St0cjxdBZ6/F7O0jIiKiAhPB5pexwwf0NN3mvdvOwvg7zna9L9ENedF3i90nAGVTV0//nl182Y/b8EXU38F+PdwtJVyIOTC8H4Hh8yokIb6KaxrFTiP0Q9wCUERERFRYYhfAuPP8I023Gbp/TxxzcG/X+zpkvx6uy1ArKtIYgRFgDgw2dPVdcsJAX/bjZgBGAtGeQnLVqUMw/38udFVGUSEGMLwu3+dTGubvoerGVl/2I/IchDkgRERERGTGnzXgfNS7q/kd2wTM71IO6tsN26ubDLdpTaXtVM2UF8Pd2VT1RpfiIhw3qA9Wbq/B0P17oKyiIegqxZLb69eP+EXvriWobQ7PnXivp83wOyXawhwQIiKi6CkbPTLoKlCBid0IDKuNM7PNrAzDFh/AyL87xrtl4ZRIJPDKf52B139+Bq46dYhn+1EiPYbCHSuBRjPFHvfW/vCdYXjvtrM83Ydd7Yfs1aF7eUq/cXj//P15t7vIEDsCg4iIiCi6CjKAkUiYb2cleWJrSmznUvSdUyvHWWi6FIu55BMABvTuihFHDfB0mgJzeLrjdT6IE4f0DV2eDavfI7eed4TDPfB6j7RwXa5EREREtsQvgGGxdSaiY3PTOYcDAI4b1Md1WYBOwMF1Dgwuo9rulEP7YegBYvOWAN6OknHbnyv0VUz8CC6kQ3aOvf7celm+1pk8+bD9vNshgG6lxZ6WL4LI7xiO6iMiIqIoi10ODCttMysNOCsd/5+f/TUc3LcbTh/aHyMemWyldq73Sc4dPqAXVpRXCynLr7eqW0kRWpLOpirF4XIKew6MBICvHdDL253YZPWQnZ4aT0+pRgTjvKMHYL8epdjXIDZh5sXHHoTapiQuPOYgoeWK0qdbCWqaxOdWicP3AhERERWu2I3A2CIomWKXEvNT0620GD84ZQgO6W98V/8IC0u7Apn5+iLblm7LitudOpGdWfW58bJDcPdFR7t6fZSDYiKq7scqJKGbQtJWH7PPb7jGjWRo5XxJJBL4+tf2F76v5288DeNu+kbo3j8A+PWFR2OeagUe5sAgIiIiyohdAMPSsnYWWnD/vOZkW/sd0Lur7nP/O/JYS2VoNaQLqbH5g1MGe1p+AolIrfRy23lH4CdnDXVVRtSnkLh9u7xekSOMH1CrVXI69cWroNj+Pbvo5sCIcBzOkeMG9fFsakuUg5pEREREsQtgNCdTQso5YUhfHNCri+XtP7trBF76yWm49oxD856zMpqjnejGpZvi/G7nnnZY/goEIiUSQJGoK151brw6T8cO6mP7ejjl0H7eVCaiBvbpFnQVfGc5aOMwtuXV10IikXA8KiSEgyhcOX/YgVn/DtPIPCIiIqIgxS6AcekJB5tuY7V9X2pjxYr9e3XFBccchBKtURQW96fVuS6ku2XeJx8UNwLDj7fF7hSe4Yf0w+ED1PkYCufa0TOwr7cBjDBOs7J6bTofgeHoZRYojkcMHba/tWl6onl1LnKnPvXrYT2YbqaAflKIiIgohmIXwDhuUF9M+NXZOPJA94n1RLXzrHZyikTnwEi462DFraGbWeXFiykk4ThRwwb2DklNxEggUVABPLte+slp+OFpQ/Iebz9nZqcu7XQEhkdviaI4z8vxwo2nCa2LVV5fnZcPH4TS4gT+8J1hwsoMy/cVERERkROxC2AAmSCG0dBxy1n6fe48/XLE4fl18LUGufuOV0O3KCFuqLm6GPaxC5eT917U9XLBMQdhcL/8BMJWr3HHIzBsfi8M7tfd0nYKoJsDw8x+PUqdvdAlrxOAPv6j4Vj0p4tw5hECk5jy+4qIiIgiLH7LqAp02P49UF7V6Locqx2WK04ejJdnbnK9Pyf7duuEwX2xXNASpV7xKoknkReev+FU3PT6QtuvsxpgcJzf1eZH6NWfnY4LH5tmoT4Khu7fA0u2VuXv0mSfQX2uS4uL0JoSk3dJSyKRQO9uYoMz/AokIgqHstEjg64CUSTFcgSGGasjK/529UmW7x4a7s/FdkE2Nu3s+3ffllzvz+sFMzJTakSV1VmSiGtElIaWzs5UyukcgQg4fnAfAMD3ThoUaD2cXE9WO9tW7u5rFWV1UIDTfBN2j9nOSLY/XXYsLhh2IB6+8gSb+7BZKUG0ch6FXfRqTERERNTJ1QgMSZKuB/BczsM9ALwoy/JNbsoOg8H9umPcL7+Bc/422VU5VhvwiQTwyJUn4qpnZ2PkiebJSE3L83ESSK9u7gfz5A5p//WFR+Mfk9a6Lrddkcgknqq/Lz5uIP582bG4/+NVQsru2IfNqioK0JpKd/x7yH7dHecUCAOj43//tm9iS2UDBvTuio+WbvevUgKI/Ez26pr/ubP6feN4AIZH0QIFmWTIL/30dNuvDWq6m51Ez2ERhbwycW9bEBERkXOuWl+yLI+VZblX+38ALgewE8D9QmrnEb+bb3bai6cN7Y+lf74YT117su3Xut133ms1HrvxzMMsb2tXbgCjpNiDhJsevPnFRYm8ZQ+Doj6HXs/PD1JpcRGOGNAr8LvJTjqDIq/B676ev2yz5VVUfVpG1cv3qFtpEX51/pFIBBRH8OI7yor2EUhxFdW2BREREXlPWLNPkqReAF4FcJssy9tElRsHVvuR7XcR+/YoDe1dsitPyV/1QJRkKrtHNWQ//akZ0373LdvlJxLi5srnFhOWtyuZLowARjsRn5PupcUCamKdnRFZZrqVFmNA7662XweEbxlVJ9VZ/pdv4+6LpcACWUGNwHjgCuMpNgfmXBNqUftWYNuCiIiI1ES2vn4PYLksyx8ILNMTdhrgYhrrLpYyddnc/OaRBzh+rVZ/Qu98iOhI5uZsuPQE/Wk0h+6fv/qCmaJEQljnK/d9CcuKLepzGMX5+X77yZmH4f7Lj9N87tbzjjB9vaNVSOy/xFDu58ZqkM55Dk+PppAYRDD09tkeQAgq4NsloACGm492WIKtNkSmbUFERETeE7IKSdsdkjsBXCKivKCNumRYIPsV3bBMJDJLyr5985no270U337cfCUAtZZkOu8xvY6EiKonczpipcVFOOrAXli3u05A6UBtU2vsVyFR31UvKoAAhtsj7Nm1RLPze9ph+xkuxSxq/yIkU9mf0/Y6mV3qjqeQBHDQikm4JahLPagRGGZBJKP3KCzBVivi1rYgIiIi90Qto3oFgM2yLM8RVJ6njBpw3z95MG451/zOq639BXy37Iyv9Xf0uuak9eUBRdQzlc4PmIhMQnnUgb3xzSMPwIz1e12X5ccUEidFxmkERv+eXTzfRxBJTkUH0XJHYPTpbm3ZTb9WIbG6FzfvRWBJPEuC2a/ZJWR0PiIWw41U24KIiIi8J+r20XcBvC2oLCHC1EgLUVVsaWrVGIGhN4VEwFG2pvK7ME47WVoO7NMV3ztpEC4fHuzSm15Sx4CinAPjiAE98dNvDjXdLujPuaMpJDZz4pjJHbn0m4utLWnsNAeGm496zy7O8o24GXGg5ZiDxSTBvOR496tFecHofAQ17cWh0LUtiIiIKFiiWjLfADBbUFlCGLXNjYfXiicyaZ+f/M4V0tCSzHtMYPyiLQdGAuccNaDjsf/cciaev+FU12WH5b1L5axCIvL8+enL35yHA3ubT+FwS+9t8/L9FP2e5I7AKLUYuPLr2lDvx/C70EV97L5fJw3p63xnKpccP9Dxa685/RDHr3VzfUZsalno2hZEREQULNcBDEmSigEMAbDDfXVCICRTAYTs18WOzz16AL7xtf2Flmmmor4l77GUwF6W1tD9nl1KcNpQ+1NsnJyHm889HN84vL+wzlMuBUqkVyFpn7r17I9Psfya4Ofzm+//wmMOyvp3UmOqlBu5IzBK2hNbmtQt7XgAhjfnfLDBqkNmu7RbJ1FfK26mAxmtFGLGdESK45LDI3ZtCyIiIhLCdQ4MWZZTAPxdh9ACp+1Kt/PTtZLNiR4y7rVzjx6AV392huZzukk8BVQ9rdGjyr277Eb7yGlP8lVYKPR7Jw3CPZccgzvHLcbSbdXiK4Hsc1hSVIREwr877W6NumQYbj3vCPS1mMMhKm488zBMWr2r499aU6U0ObxOrQauHOfAsF0v4/1cfeoQfLpiJ+79rvZqMBaKQGlxAicf2g8ryqutn18B3PxeuFk5Reul+/Uoxb6GVtdlh0VY2xZEZKxs9Migq0BEMRepybB+8GQKicVStdqcUWmIigi+aPU7tIIaTumdSyc1z19G1TqrHUe7b30CiayAT3EielNIoha8cPLxPPbgPq7uvuf6ek6S3tLiTKXMVu5wOrqp/ZCfvv4UfO8k9/lkRl0yDEvvvRhnHpE/4stynRIJvHPLWVjwPxfh8AN6Wtje8a6EleNmhJTWfouL+HNORERE8VeQLR4vcztodeQjEoOwRDeJp4Bj1CrC6ykkZp08PW6O18uYgjoxY3FxdC68EUcd4Oh1Xn22Ekh41snt3qUY037/Lbx985lCyr/v8uyRCyUWO7KOp5C0HdClJxyMf157MrqVGu/PykfYtDOvevr6rx8KAOjVNXsAYXFRAn17WF2BxdJmptzkk3Azw0vrd0ZdXpx+c4iIiIjUCjOA4eESc047xIB2B95ddcS3Yr0MYGitDJASmC5AL/m+kOCLhTI6rjuPIhgKFFx2YmZVhP16lKJ7aXRGXz9xzcmB7btLifOvQbO3/Q/fGab5mm6lxaYdf6uGDeyDG75xWMe/O0ZgmFxnTkc35V7rZvs5qG+3jjqdPnQ/jfLsfQB/fdHRePr6U/Dlb8619TovuApCCJ5Con5sUF+DfCJEREREEVaQAQwjXuShCOPdsP+59BhHr9PNgeFR/g7HSz1qEDkdJ7ckO8fvJshl5pZzj8BrPzsDn9w1IlJJPPv37BLYvs8fdiCGDeyN0w7L7lyLuPRuPe8I3efMys9994zeT3Vi0BKLy2Q6/Wz1sznNp0+3Unx61wh8ePs3cfiAXnnP271KS4uLcOkJB+OgPt6vUmPGzfeeq/wZJuWNujQ/cEZEREQUBwUZwDBcRjWR+2/3nUDrOTD8m37yy3MOxyNXnqj5nJNujYh6aiZAdV9sh/YGft57bGEvvbqWYOj+PTpfk1OIneO3229sHzJvRUlxEc45egAO5h1Yy3p1LcFn/30O3rn1rM4HExZH1VjYSO/6svs5K1EFMHJjGeVVTR1/Wx15YzdB7iXHD8TfrjoRRx3UO+txK6UceWBvnHRIP83nRH/H+Zn2xU2M0GKcSZPmb4Xq71MOzR/pQkRERBQHBRnAMOLNChXiyxTBcNlCHbpTSGyW07tr/gI4Wh37Z358KroUF+E7xw20uYd8Tjsbpw/dD4v/fJFuB8yq9nPXr4fV0QaZFzxwxfGu9htnXn62vP7Y2l0F5B8/Gt7xd+7de/W/+rXlgdAqXp1rxO4IjD9eegyuPu0QW6/JpbXLsKy+5IiLqrtbwST/MevfK0RERETRVZABDONmo/GzZx5uP1O+9WVUtR4T28h1Wg+z5+zs641ffB03nHlY3uNaHbozvtYfS++9GH/67rHWd6CjWCuJp4K8g/r+yYPztivNuV2aP4XEut9efDSOG5Sf70NPVFaiiR1LoyucF2M3BcWlJxysW6a6qPaOcW6A4oBeXTF0/84VOr4tICgICAj0WMofo/rbo9FeTuQGIS4fPgif3jXC0Wvt0HrlHy4ZhmMP7oPbDKYtEREREUVdQQYwjJi1KR/70Un47cVHY9Ld51gv0yRjvNV92+W0OKOmvX4dre/trCMP0F4RRGfH3buISUbZHggwCgp9/+TBWXe61dur65dXfRsne/9eXTHhV9Y6Oe0e/9FwDOrr7Zz/C485yNPyveDV3fsEvB+BYTbZwShwlfucOvjX/pRW6eqXffv4gXj952eY1tKMnVCAl/lf2vkZ78vd1T9+OFwzGbEW0QlA9+/ZBZ/cNQK/10gcS0RERBQXBRnAMOwYmPy7X/cuuOP8o3Dkgb1hldburj3DWl6DqNx8F3NX1Ft6HQZ13Z0GS7weBn/FyYMx654LPCv/d9+W/r+9O4+S4yrvPv6r2VdpFo02j3ZprjTat9FqbbaEbFm2sY1XBLYExjbewRu2MYQACgkEDDGQBIghEAiYsPllCSGLIRA4AUPeAAWYKCzBgIMxBstY1ih/dM+ouqe7uvaq7v5+dHTOTHX1rdvV1T33PnXvczUYYEpR1rzpwpWRleXlDrm3PBmlfw+TJLT4sAXBNY9lNFiWTl00UPbxN5y/omDKSWxL1kZc7lXbkxuBMGEqj4/XEibJbsnRelXytwIAACCMugxguKnUCAzSSCz1lJfvMSXK9ld4gyW1hMkE59FzlubuzL/mnKUq1z2Kou3s1qGLovyGfIdhh8l12hobLC2cWrgqglsdnA8FmdYRdwcjwgVbqobznG4bGtB5awZjKduP6UWrY5QLhIR5u9yCK2OPVcqxUenlnT48TVsWOgMY4S/g0jkwonX+mkG9qsKUs+42fyuplBPmlES+jGo15xIBAADwaGImxTrgnuMh+kZgqcam1/nPbnfp/vKF6zQyr19nvuUh/ehXT1Us6/pdC3XvF36gnab8XddS/uzSNfrRr57S/IEuPfLL35bcJ5LOTcxjMMbOeU9Hi75x9241NVpqa27UseOjjr2C1aGekr9mlZfTtWJwsr71kycql2V5zG9RYq/i9634M9yWXyWk0g14t4eLn+v87Iwd32+OjUrHj+tyjDrHS2ODpVOHSn/HbZjXpyeOHtOBjRNz8AQRpu5hcmCEeS4AAEA1q9kARtCGZRwjMEo2/T2W47YkoiVLXa1NnqZGSNJNu4e0d9mM8VEH5apQfOe2qbFB8wfcnxOFsB2uSpznqbfzZMb+aJbKrW6WVR8Bk8nt3u+8B5keIkmHts7THz74nfFjFX8+X3NOblWZFYM9Wjy9W8eOj+qRX/7Oc71yxy0sdHS01GPRLksc2xQST8c+uVeYarzl4tWa7jGXTE9HszqaG/U/Tzxddp/i99bPd0lTY7QntB4+v0DSjhzel3YVAABFanYKidvwabeG3lbHkOlK+3oVpgy3nAxj5Xq9G2dZloZnTlJLU/Rvu9+XWLLKAd8zr8LetfS77GUxhnhHz+8Z9TPlKuj7dcWWebr/4Ij+4WXbc+U4rrt79g9r7pTcSiDNjQ369A2n6u9v2u77GIGmsvl8jtdRKGEHTsUyeqnMdj9pJ/7qipGK35Vhgp+9HS26eH2wZWlLTiHh6wUAANSBmg1geLFn+OSqCxetm6V7L1mt3cPuKzEE6dSESbjW1uQWwLB8lTWxgABPKXOw6kjiGTB/h6c78dXde7Dy/2qd1+CdJa+994kaGyxtHxrQlK7W3O8VVhNpCJDMsfhaLjX9qlK8zXdAo4quj7Kfx4hfQqiVRCQdPn9FsOeWeH3V9P4AAAAEVZcBjLHG33W7Fo1vWzY4WWevnFmxI1qp0f/c1ROTCJZubHrT3lL+LRorI8n50OWOFEXjeTTmLJResv6XqsJte3MJV12Xlw1YpyTlkrCWVq05PPwGjlYM9hT8nsR76vx8+rnE3V5a8WOlpl+VXkZ1YqFu09QKE9eWr08YSXa8/RzL0sRzeNe+Jdq8oD9QeRPKDxn8iLI8AACAalGzAQwvHRtPc9x9NlDXzunVJ6/dqvVzex1lBNfqMgJjrGMUNIAxu6/D93PK3tiMoPG8af6Uso9F0clZMLWzdNkVil47p69i2UHzJbju72/3ig5smut+vAQ6QHuXTo//IC5esGlOwdKgbuJYRjWqEJ2Xuo16TCrzvkMj6u2YmBuk+DMXxeVRahqW/6kt8QUN9q+c6fr4i06dr2bHNKTiVXCirIvb/gQrAABAvarZAIZfXtuDXvZbPjhZUx1LKZZqbHrtyHjJgfGCzcEy6g/2dugvXrBO73j+Wn34qk2ByojKfZet0VaPHcug3IJBY+pxKVIpumDJhnnuwZ4ZPd4SKHrlVu8+R6LWMZ2tTbp258KKz7csaZ0jCBmGc+RP2DwqYybU20Ox5V7rurl9+vrdu4MXkEHlqjqpwvKpwzMmnSzDKv194Bwp5gwkzZ9SOkBavo7+TqizLiVXv/FVGgAAQHUigOGT17t/VsHPwZuW7quQ5Fyyfrau3Da/xOOVj7t7eJr2LpuuBflVRiopV2aYO4J3nrlEZy6f4X7cGFvnnt8fl05iFuafh+kae07Y6OIPz12mdx5Ye7JMx2Mb5vVphxnQTbuHQh6lsj8/sFbr5/bq/S/aUHFft3M2p79yh9TL+x7HFK/i76GSOTAqleGoe9ncNh7qEnb546RGEzxw9aZQCYwfuHpikNc5K8336wjxuku9DkZlAACAelDXAYxAmfw9l+2+p9cbsW1uAYyxKSQNlrYt8jd8OajyU0jKv95LN8yeuL+HMtMQuDPmaTpSeC/cNEeT2po0z+fd3rh1tTbp+RvnqKej9PK0h7bO019dMVLxDrhfpa6dPUun68NXbdYSx930KMv3y9nJjWqET3G9SpUb+lhW8a/hT0bJvBweyo3iszNjcruv/S1ZBee51FQy5zWeZC6i0tI+PgAAQPzqOoDhRWxtUo+dC7fEk4Vz68Mu8RmO2/Nf99zl2jS/32WPyrwk4Fw5ODlQ2V7fY7dznFTf5dXnLNPX796thVMnjpgJU4VKnchLRmaVzJPgXmY2OTudblNIvJVVeR/nKiN+PqduAYjiw5baSsRIGwAAIABJREFUNYp8E1nk5SVEtcxopcCQs8izK+TPmFAf/9VxfW4tvLcAAACV1HUAI9CSqBE1Et1yWxQ7tHVeybvJWWqvVjovYQMsY0tSuvn4tVtDHUOqjhwYTY3Rf2wrvT+vP2+F7j84Uvbxau1QJfF2B12FxG3XCcuoeijYsqTdS3LLRLc3N6q50f0Nsqzoz0+pasayAk7JHBGVD+Tle8o5+smypK++4jQ9eP1WrZzV4/KsEnWMOBnp08eOBy4PAACgWjSlXYGs8H7HNUAOjKKnfObGU33Nxb77rGFJ0tzbHyzY3lBhVIKf9nHYO86VOgdxBwZ6fI4OiFrQu8JRHi/MKfayYIXHRS3GWSUXogxv8fTuk8dIOUriaQRGwUipeI5bcgRG8e8npE0L+nX/wRHNnNwWSyAsiKTewSCrfpQKaFyzc4F+9KuntGlBvyzL0tRJbQVJmz2X7/sZJ01ub9a2oQH9y/d+Ob6tGoKvAAAAYdV1ACPWxJBlyh7sbdfi6eHn5kvpjMAom+yv4giMeL3z+Wsr7+SB2zx21yH91TDcwIWXzk9UK2iEsX1oQG+4YEWoMgqWoyy3T/6RKF5y4BEYLjtPHIFR6vkTt1mWpe0+lvv0lMTT16iSUtNakvnsRHWUGZPbXUcjeTX2sv/llp368g8f020P/IeP51p678GRgqB2Bj6eQNU6cnhf2lUAAHiUjVtwGRZ109pLLgevCjti6XYCKh49gs7//vwc8x1mYgdsQ4gcG55zYPjISRAFt/5I1H2+UQ+9H7c9mkpMR/Bax7Zm719DuxZP1bQAd7vLKX5NI3NziRpv3Ws8Pd/TKiRBc2C4HdfDCIzi99T3CAR/uwcWx+il0jkw/L+iOIMCY9fO7P4OXbR+YqJjv8JO0wMAAKgGNTsCI+kh/V6PH22m+mAdo9IlhaxXhad76SBX8rrnLtO+5dO1MWRCUDfx3gz2V3ilHAXFwiwROeoyP+S6XQslle7MrZ/bq68deVw3nLZowmNrZvfq508+rWeeHdX2EkGnMVsXeh8REPcokA+8eIOeOHpM/fmcK5YVvhObxCokWb39PtBdOXeNFwWJMwN+RpMcJHXqoil66PuPue4TdX28XALnrTkl2oMCAAAkrGYDGF7EOWqh3N2+nz1xNLJjVBrMEcerC5wDw6Ugr/XsbmvW3mUzPO5dqK+zpexjzrpnqXPU31m+8+es8+rZPfrp40d14+kTgwhejZ4o/Rreffk6bV4wJf/bxB7SOw+s07d+8mttXThlwmNNjZY+d+M2jZ4IF1yJmlXmZymXILXfQ8LY8ed7eN8bA1wcd5817DoEY8IUkhL7hF5F1bJCl/G3L9nk4TghD+KR38OECV699ZLV2v2n/6JfPvl7z/X5o/OX6/aP/oeu3xX8c+ymv7NFrz9veSxlAwAAJCU7vYqIzR/orLyTF0E7tGW2NzVEd8ojnTvuNYlnmR0rVeX8NYM+KxStf7plh8c9g53TOIJhXkfrvPmiVfrKHadpanfwqRXlRsjsWjxNbc25FXNK7dLX2aIdZmrZhJBNjQ0Vgxdxd2D3Lp0uSbrjjMW+nxvFwAbn59TLCJK9S6fr0NZ5rqOqvOXASH9UhnPFDql8Xo5K/F4jna0TY/NJ5qnp6WjRp284Vatn9+jle4Y8Peei9bP1zXv26Kbd3vaX/J2XVbN61NrkffUrAACALKrZERg37x7Se750xHWfNHJIRCmuGrsnqyyzvUKZF6+fpSldLaWXg03g1He1lL/UPefACDtNJ4J5/OVUWpGmEi+d3fS7w8E6oW+7dLV++NjvtGhqV/T18bCPM+9Nu8t1OGbsOvOTc6XUtVm8JdCy0b6f4S6pa6ivs0V/fMEK3fKRb41v8/IRiTLmM6WrVX93zRZJ0p987nsTdyhRn0lt5VdTesGmOXrvl/9br8yvSjVWxFiVK1W92hMNAwAASDU8AqPbpSE4Jo3m3HFHroEzlk0PVVZDwTSMcK+mIJgToKjixnFX0R3QhgZLe5ZO16y+jiDVi1XBlAKX1x4ksBOG56VtI7iSvSyR6rdz57XD9Jyl3j8HQUYVNDU2aGha93h9olxe2EtZvR3N2j40oDn9HTrfQw6CWb2VPyMTknh6mEMyPNPf6kdeT5PzMNfuXOjrGF4VTvvxVrPnrZulK7bM9f28oPv75bf8V5+9VA/dulMHt847WYaP0T2Xb57r63gAAABZVLMBjNSVaZsedzQy33jhynCHcCYHjHB5QrfnBV6FxO14IZ4btSzVJdqEr+48rULiM3jgpfZvu3S1zltd24kFLcvS/QdH9E8v36GejvK5WMZcuX2+JH/L9pacQuL4Tmhpagg0hcavlz/H2+otfkUyMCJLH24FGZFlTQgAO4twC0I+eP1WbV00MU8NAABAtanrAIaXBmTQu3DFzztnVW4J0DdftGp8W0dLk6dhzUlzrZLnUQHVw9kZzFIST7cARvTLqEazj19nrZgZevrLmDjeg8oxG+8H9RpQHMtl4nbo4lNWcgCGY+N7Ll+vRdO6PR0/V4fW8dwn1SzM6iVxxw+jKL4giO1ysS6dOTmCowEAAKSvrgMYcXazixu/f3phLtHimcuDraJRSpR36L2WVCqgc0pPu7rbaiOdilvAKvSqDj73TzK45WV0RWuzv6+L7E65z2zFCri9JxOTeE7c17mPl++KZaecnGLymRu3FeTuCKK7RCLNoDkmIunse9jHy3mNShQ5KVYO9oz/vGAg+hwvAAAAWVPnAYzkNDRYmj554ioRYZrHcXUQ/Zb79zdvm7AKRcWEcgXHS7dDGU3nKPrX4DqVJ+rDeShv9ayeyjv5K9K3tK+VYhmrToEtC6dowUCnzLRurZ/bW3H/t1+2Vmcun677D46MLzt8+vC08ccnt1fOKyRJrzl3mU7padd7D40Eq3hMvARxdg9PVUdLo2ZMbtPc/ohWsiojimvH+Tel12WpaAAAgFpRG7fNMyiJfk2kq6gWJAT1d8wODysrpM1zQswMJfFMcgTG/hUz9fGHf+q6j9/gQRzBhqjviFdeuSHalSmi4mUZ1ZamBn3upu2y5G2Vmll9HbrvsrUF2xYMdOlzN21Td1tT2eVwi9+TAxvn6MDGOWWOEv5kxjnNa+HUbn3tztPVnF/+N863PsOxL6DAkcP70q4CAADjGIFRQZZyIhSrdEcxeN39J/EMI+272IXL6QYsw9Nx0g8AlLPslPqZI+/ntFYKXsT5Drkd2utraGywQucYGZrWrRmT20OVkQVeR0l1tpYP1mRNBmNrAAAAsaqOVlqVC3pXv2K5wZ/qWpb7CIzavm+YpdeXdIJXv6/9Yy/d4l5emMokJOo6jszti6wst++GCSMwUuzKTp80cWpcOWmOZgny0Y6zvhn6qgEAAKga2R/7X6XiyIkw4Rgp5MCIZQRGDGX6Or7nE1m+NxNH4MNrkta0OkKrfObEyKLQiVnzJ//zN2/XJx7+qZ6/qdzUCf9Wzio/KqY4uBXHCjFe/eUL1+v6D35Dh7bOi+0YUXy+shcwyFyFAAAAMo8RGBVkuYkZZae5sKjw5caZvT9OgafdRLSPk9vQ/6ABsj8/sFZdRatDvCDCTnea4rjkvF4PC6d26eY9ZnwJ1Cg4p220Fk1p2G6mRnacsIZnTtLnb96uS0Zmp10VV0kElcsptaJLJF/f1fk1CwAAEFjdBDCmdCWboT2Ju32VDhG0we46AqPosaBLLRaUk71boyUlncQziiJn9RXmLtizdLq+dc+egm2vPntpBEeaKKtvq9fpUn7LitPYufzYS7foFWcu1jU7FhQ8Xq0BwySleT1+/ubtetnuIV23a+HJ+sR8zMs3z5UkvfKs4ZiPBAAAkJy6CGBsmNenVbMqLyMYpUQCGDEdxDUHhuPRjfP79JU7Tiu9X8Z6r177d+euOiXeivjgdQqJm/dcvl7r5vTqrZesPllug1UwBSG+9yrZayBQjoNKjycUF7jx9EWSpDdduNJ1v1WzenTltgVqa24s2F4t8YtUc2AEeE5UuUXmTenUdactUm/HyUB6FJ87t/rds39Y/3r7Lh2McWoPAABA0uoiB0b5dmJ1L5IXbRJPxzKq7hGMcZvmT9FAd2uEtYhWd2uTJrU3a8Xg5IorMXz1ztP02JPPaHjmpLL73Lp3sf7hu7/Q5gX9Ex7z0hnx219xrbLnqQ3d+sjVmydsP3z+Ct36kW+N36WNQ8ZiWLGI6jXeePqQrtgyT5PbmwM9f+OCfv3wsd9FU5kYJZ1s1DkyJWtB1bhrY1mWZvZU/+oxAAAATjUdwFg/t1dfO/K4bt27WPf94yOu+5Zr22at0Ttm+SmTNauvI5ayk54rHtfRJrU366Fbd3paRnJqd1vF/AVmere++co96mpL5mMT57V34bpZ2mEGNNCV3QBUXJznNUufbrfgRaXP5B1nLFZ3W5N2Zig3RpSimHEWZLYbq5AAAABkS00HMP7mxRv1+FPH8qMESrVET7Ygo26oHh8dHf+5qSH6mTqfuHZLxQ6unwayc1+vz0tz6UYvTpw44Sl44cfkDu93yIdnTNK3f/abwMdyq3oUryrKhJOlVEP/rNIVbFkVcp9k5FV2tzXrjjOWpF2NiuK+5txkIRgd9TdmtUwdAgAAiEpN58BoamxIbYrD0WMnAxjtLY0ue/pnWd4a40GXuSxepaL42F74SSoYV78i7bZ9Q4P0st1D47/77ey65cDobjsZSIkqSOMsZWhal/72JZvClZd+fzG0rHQQ181NNodPXK7esUDbhgbSroZn0QccHFNaIlntKXQRAAAAVaWmR2BUFl/r7+gzz47/3BFRAOOCtYP6yL//RH926ZoJj22Y169Zfe0aHZXu2rdEP3n8qM5cPsNz2W3NjdphBvTwj3+tQ6eWT/rmbDBn5e5zOVlo3IcJLrgFMF64eY6+8aPHNTStWzMnR3NXe+kpk/PHld53aIOmTUrvbnmcIl2FJOaPwAdetEEff/h/9LLnDFXeuQp0tjbpvQdHNPf2B9OuSirm9HeO/9zbGSzfCarPkcP70q4CAAA1o84DGCeVzYERsLyjx46P/9zcGM1Alz++YIVu3WtKDsNuaWrQP9y8Y/znIN5z+XodHz2hJo/1DTOFpCBpaEyBkKxPcRmzcnCyvvmTJyZsb2osf14WT5+kz9y4LdJ67F8xQ/OndKq3s6VmgxfFsn6FbF44RZsXTkm7GlXr0g1zdP+X/1udAYPIUQdBdy2eqsPnLVdPR7MGe+PJYQQAAFDL6iaAUakh6qWh6meFgAvWDupLP/hfTZsU3RQWy7Jc55AHDVw4y3frNOf2CXWIRCU9AmNuf4eO/O9T479bsgLlFpGk89cMqtNlKk8cLMvSsvwojEjKy/gIHS8q5cBA8vxcV2Z6t7542071OJYvTVNjg6WLR2ZHVl61BGkBAACiUjcBjNL8dbCu3rHA8777V8xUa1OjFk/v9lupmuAnYV5cQZHRhNv2f3fNFv3PE0e1794vjm8L2ol/2Z7qnzKQ1WBXQVCpwr6VghdZfY04iZEOAAAAtaNuAhil+yGVe7g9Hc3aOL9PRx57Ss9bO+j5eE2NDb5yUFQL7kaX19vZot7Owju9njq4JXaqhY7x7uFpaVehIi7nKlEDn4c48H0MAADqTd0EMCopmwPDsvQ3L96o0RO54b/wxtcqJDHVYenMSTGV7I1lBX9tbgk8s+6zN27Tdx/9jfavmJl2VSL30Ws2653//Ig++58/l5SNpTkRJyIEAAAAWRI6gGGMGZT0DknbJP1G0hts2743bLlZYlmWKqSGqBvV1F/74wtWpF0F10BEW3ODnj42qss3z9FNH/p1wWNVdJonMNO7ZWKaOhVFd7IwgWyFfYtyYPR3tmjG5PYIaoGgquk7KG4XrZ+lz33752lXI3L10K4AAADBhMr6aIyxJH1M0nck9Ut6jqRXGWM2R1C3BJxsCTMU1xtnh7y9OZrlYaPU4lhBZWoGVtJw62x96bZd+tCVG3XuqlNKPDG+OlWz4wknNqmYAyOZaiAlWf+7sGvxVD1w9WZ99c7T0q5KZKq/XQEAAOIUdgTGBkkzJd1u2/ZxSf9pjNkk6bHQNYtY6SkNGW+dZlBXa5POXjlT3/v5kzqwaU7gcoKuzlHJ3161Sbd95Ft66a6F0RUakeLX2d/Vqv6u0qvUVPMUkjgdOx7tZ9ZvacUrywBpsixLa+f0pl2NqFVNuwIAACQvbABjjaT/lPQGY8xlyg31fK1t2/eHrlnC6JR4d+8lq9OuQlmrZvXoszdtS7saknJ354PmSOByLO3Z46Ohy4jys873Rm0jxJ2KmmlXAACA6IWaQiKpT9JO5e6MzJZ0uaS3GmNODVlu5O7cN6yWpgadviT7KyPUm6BLjVYDZ95XP8PRGYFR2rGIp5D4Pcu5xKy8N0njnNeVqmlXAACA5IUdgfF7Sb+ybfv1+d//1RjzgKRzJD0UsuxILZzapW/cvVsdLdnL24DsWTy9W9999EnNn9IZqpyg3S7iF6WduyralU3ChkPoWCePM17zqqZdAQAAkhc2gGFL6jTGNNm2/Wx+W6My2sbsbGXV2EzK4NXy3kMj+tg3fqpzSiXY9Mqygk8hIYJR0vyBrrSrQHCpjrzj+Wt12V9+RZeOzE67KvUk1XbFkcP7kjgMAAAIKGyP/u8lPS7psDHmdkkjkp4raXfYiiVhoPvkKhUrB3tSrAmyZmp3m67ctiB0Oc7O7qiPOSR0kpMRZAqJ2++oLSPz+vTwK/cQ/E5WVbcrAABAvEK1ymzbPmqM2SHpbZJ+oVyyrett2/5KBHWL3eT2Zn3kqk168ulnNTxzUtrVqVu12ge0JG0fGpBlSR3NjRroLr3iSLnnIn5BppA4l3IlV0ntI3iRrGpvVwAAgHiFbpnZtv0DSXsjqEsq1s3tS7sKdaleun1z+jv1+Zu3q6OlUR0t3j9udIz983rGwpxay7L0+2dProTS1hw2DzL8YnpV7av2dgUAAIgPt5YQC5YfPGlBgLwN9NGSEeQ0//7Z4+M/tzWTFBgAAABICrcPkTruqE7ECIxk+A20WZJ+f+zkCIzmRr5Ck8DHAQAAABIBDGTMOfllMl999tKUa4Ja5QwO+cirOs45AgMAAABAcphCgtQ5b67+6YWrdPPuIc3p70ytPlEJc9eYERjxcZ7aEz7HYFiWdOmG2fr8d36h5kbeIwAAACBJjMBALIJ27RoarJoIXkj+zsFfXbG+8Ln0jWNjqSCC4dtOM1V/d81mffmO06KrFDzjowEAAFC/CGAgFpX6hc4OOp11aYeZqhHHijiMwIhPQ4j4hSVLlmVp9exeTenyviwuAAAAgPAIYAAZ4ZzOkNXwxay+9rSrUNa0SW2e9iuYQuIzCQZxpXRw2gEAACCRAwMZQKdwoqyek/cf2qi3//MjumzD7LSrMu6OMxbrH+1f6La9iz0+I1wSTwC1a+7tD07YduTwvhRqAgAASiGAAcRkRo+/0QrOznRWl5ad3d+h15+3PO1qFHjJ9gV6yfYFnvcPN4UEacvoRwMAAAAJYAoJELF79g9r4/w+vWq/v6VgGQyQDCvEMqrtLY0R1wYAAACAVwQwEJnnrj5FknTY5x16K+B97Zdsmy9JumvfkkDPj8sVW+bpg1du0kC3vySPfvMxIBjn1eZnGdV3vXCdutuao68QAAAAAE+YQoLIvPF5K3Xz7iHN6uvQH3zq27Ef7/YzFuvApjka7O2I/VhJIHyRjAYfIzDmTenUfz32O0nSaUumxVktuGDaCAAAACRGYCBCDQ2WZvV5CyY4h/EH7ZxYllUzwQuJhJJJ8XO9veacZepqbdL1uxbGVyFUVA35YQAAABA/RmCkbNfiqfrCd3+htub6iiUdHz3ZIzn6zPEUa5IdxC+S4WcZ1a2Lpuib9+xRYwOdZgAAACBtBDBSds/+YQ10teqslTPSrkqijh0fHf95ps/VOmoWQzAS4byDP+rhlBO8SB+DLgAAACARwEjdnP5O/dEFK9KuRuKOHT/Zc+xsZWUHiREYSaEvDAAAAFSn+pq3gMx41jECo6mByxDJKUjiSdgIAAAAqBr0HBGLSrMhnnWM3W9q5J64xAySpDinI3iZQgIAAAAgG5hCglQ4k3gyAiOH0QDJcIbLCBoB9eXI4X1pVwEAAIRAzxGpYATGRHSmE8LlVnUs3jQAAACIAAZS4syB0cwIDEkEMJJS2BnmpAMAAADVgp4jYlFp2UPnCIxGRmBIoiudFJbkBAAAAKoTAQzEotJogqeeeXb85+YGepSSdIIhGIkgBwYAAABQnQhgIBXf/PET4z+3tzSmWBPUG8u5jCoBjFR86MqNOnXRFH3i2i1pVwUAAABVhFVIkApn0KK7rTnFmmQHnelkMN4nfRvm92vD/H7P+zPtBwAAABIjMJCSN164Ut2tTbpu18K0q4I60+AcgUHmEQAAAKBqMAIDqVgzu1cP37NHjeS/GEdnOiGOS26UUw4AAABUDUZgIDUELwoxhSQZTEcAAAAAqhMBDMTiwnWDaVeh6hC/SAarkAAAAADViSkkiMUdZy7R4hmTtGXBlLSrUjVYRjUZFjkwgLpw5PC+tKsAAAAiRgADsWhrbtQlI7PTrkZVoSudjIIZJJx0AAAAoGowhQTICjrTiSAHRvXhPQMAAIBEAAPIDOIXybDknEICAAAAoFoQwAAyghwYyXDezeecAwAAANWDAAaQEWevnJl2FRJx/8ERLTtlkj545ca0qwIAAACgipDEE8iIl+5aqJk97Vo3ty/tqsRq+9CAtg8NpHb8ghEYqdUCAAAAgF8EMICMaG1q1MWs3BK7ghwYRDCqBFk8AQAAwBQSAHWGFS0AAACA6kQAA0BdccYvGIBRHc5ZVR/5YQAAAOCOKSQA6oplOaeQEMKoBhvn9+uj12zW9EltaVcFAAAAKSKAAaCuMIOkOq2Z3Zt2FQAAAJAyppAAqCusQgIAAABUJwIYAOqKRQQDAAAAqEoEMADUrRNEMAAAAICqQQADQKbtWzFDknTXviWRl00OTwAAAKB6kMQTQKa95aJVunn3kOZP6Yy8bAIYAAAAQPUggAEg05oaG7RgoCuWsplCAgAAAFQPppAAAAAAAIDMI4ABoG4xhQQAAACoHgQwANQt4hcAAABA9SCAAQAAAAAAMi90Ek9jzC2SXivpGcfmM2zbfihs2QAQJ6aQANlDuwIAAJQTxSokqyS9wrbtP4mgLABIEBEMIINCtyuOHN4XYXUAAEBWRDGFZLWkhyMoBwAAgHYFAAAoKVQAwxjTIWlI0g3GmEeNMd8xxhyMpmoAEC+mkADZQrsCAAC4CTsCY5qkL0l6u6TZkq6U9CZjzBlhKwYAcSN+AWQO7QoAAFBWqBwYtm3/l6Ttjk0PGWPeJ+lcSZ8OUzYAAKgvtCsAAICbsFNI1hhjbi/a3Cbp6TDlAkASTjCHBMgU2hUAAMBN2FVIfivpHmPMDyR9VNJOSRer8O4JAGQS4Qsgc2hXAACAskKNwLBt+3uSLpT0SklPSrpP0hW2bX89groBAIA6QrsCAAC4CTsCQ7Ztf1LSJyOoCwAkihkkQPbQrgAAAOWEXYUEAKrWKBEMAAAAoGoQwABQt7paQw9CAwAAAJAQAhgA6s6hrfM02Nuuu84aTrsqACL2xdt2pl0FAAAQE24/Aqg7d581rLv2LZFlWWlXBQAAAIBHjMAAUJcIXgAAAADVhQAGAAAAAADIPAIYAAAAAAAg8whgAAAAAACAzCOAAQAAAAAAMo8ABgAAAAAAyDwCGAAAAAAAIPMIYAAAAAAAgMwjgAEAAAAAADKPAAYAAAAAAMg8AhgAAAAAACDzCGAAAAAAAIDMI4ABAAAAAAAyjwAGAAAAAADIvKYUj90oSY8++miKVQAAAGE4/o43plkP0a4AAKAmuLUt0gxgzJCkyy67LMUqAACAiMyQ9EjKx6ddAQBA7ZjQtkgzgPE1SadK+pmk4ynWAwAABNeoXAPjaynXg3YFAAC1oWzbwjpx4kTy1QEAAAAAAPCBJJ4AAAAAACDzCGAAAAAAAIDMI4ABAAAAAAAyjwAGAAAAAADIPAIYAAAAAAAg8whgAAAAAACAzCOAAQAAAAAAMq8p7QpEyRizWtI7JS2V9H1JV9m2/ZV0a1WdjDEjkj5m2/bM/O+9kt4taZekJyS92rbtd+Ufa5V0n6TnSjom6V7btl+bf8yS9DpJL1LuenuvpJtt2z6e7CvKFmPMVklvlLRY0mOS3mDb9js5z/Ewxlwo6dWSZkn6b0l32rb9Mc53PIwx0yT9h6SDtm1/yhgzV9K7JI1I+ply5+pT+X0DvQf1zhhzi6TXSnrGsfkMSf9fdXhN8/c/XVG1GRBe1O0LhBd1GwTRiaq9gmTVzAgMY0ybpE9Keo+kHkn3SvqoMaYl1YpVGWOMZYw5KOlzkpzn7i8k/VbSNEkXSHqDMWZF/rHXSpojaZ6krZJeZIzZn3/spZL2SVohaYmkLZKuift1ZFn+C/ATyl2jvZKeJ+n1xpjTxXmOnDFmSLnvhUO2bXdJukHSh4wxU8T5jsu7JPU7fv+wpK9K6lPu/H/AGDOQfyzoe1DvVkl6hW3bXY7/D6kOr2n+/qcnhjYDQoipfYEQYmqDIDpRtVeQoJoJYEjaKWnUtu2327Z9zLbtd0v6X0l82P15hXIf2PEorzGmS9K5ku6xbftp27a/KukDkl6c3+X5kl5n2/YTtm1/X9LbJF2Zf+yApDfbtv0z27YflfR6x2P1ao6kB23bfr9t26O2bX9d0j9K2izOc+Rs2/6epGm2bf9r/lqeIelJ5e5cc74jZoy5StLvJP04//sSScsl/UH+u/nTkv5Z0gtCfrfUu9WSHnZuqOPvav7+pyfqNgPCiaN9gRBiaoMgAhG3V5CgWgpgLJb07aJttnLDSeHdu5W7s/c1x7ZFko7Ztv1DxzZb0tJ8tH+aCs+987xB53UfAAAD5ElEQVQXvy+2pOH8cOW6ZNv2w7ZtHxj7PX8OT5VkifMcC9u2f2uMmafckL/7Jd0paYE435EyxiyS9DJJVzs2L5Z0xLbto45tY+cyzHdL3TLGdEgaknSDMeZRY8x38nfB6/W7mr//6Ym6zYAQYmpfIKQY2iAIKcr2Stx1xUS1FMDolPRU0banJHWkUJeqlb/7dqJoc6eko0Xbxs5tp+P34sfGnlv8WIOk1kgqXOWMMZOVG/r878rdJeE8x+fHktokna7c/OD94nxHxhjTJOmvJd1g2/avHA+5fTeH+W6pZ9MkfUnS2yXNVu6u3JsknaX6vKb5+5+SGNoMiEiE7QtEI8o2CEKIob2ChNVSEs+nJLUXbetQbq4SwnE7t2Mf9HZJvyl6rNRzOyQ9a9v20/FUtXrko/GfkvSIpIuUm3fOeY6JbdvP5n/8gjHmAUnrxPmO0t2SHrZt+/8Vba/0/RH0Pahbtm3/l6Ttjk0PGWPeJ2mb6vOa5u9/tvC5TlnE7QtEIOI2CMKJur2ChNXSCIzvSDJF24wmDiuFf9+X1GyMme3YZiR9Ox+5/IUKz73zvBe/Lya/ra4ZY9ZI+jdJn5V0bn64Guc5BsaYM40xny/a3KJcw47zHZ2LJF1sjPm1MebXyo0M+KBy52ZuPqP6mLFzGeaar1vGmDXGmNuLNrdJ+pHq85rm73+28LlOUQztC4QQUxsE4UTaXkmoznCopREYX5DUaoy5TtI7lEtINk25L3CEYNv2k8aYjyuXyfrFys33ulTSmfld/lrSq4wxFyiXyfdaSbc6HrvFGPMF5ZaBukPS+5Ksf9bkl2z6jKQ32rb9R2PbOc+x+bqkdcaYA5LeL2mvcud0g3J/tDjfEbBte7Hzd2PMEUnX5pclu0DSa4wxdyu3/NgOSdeEvObr2W8l3WOM+YGkjyqXxPJi5UZl9Kj+rmn+/mcIn+v0xNS+QDhxtEEQQkztFSSoZkZg2Lb9e0lnSLpE0q8kXSfpbNu2f5dqxWrHiyU1S/qJpAck3WLb9r/lH7tL0vckfVfSFyX9hW3bH84/dp+kjyu3JNG3lZu3/aYE651FhyQNSLrbGPNbx//XivMcufyKCvuVy5T/a0l/oNxdqe+K852U8yStVO6O0pslXWLb9o/zjwV9D+pWPqv9hZJeqVw2+/skXZFfcaDurmn+/mcSn+t0xNG+QAgxtUEQn6DtFSTIOnGiOPcSAAAAAABAttTMCAwAAAAAAFC7CGAAAAAAAIDMI4ABAAAAAAAyjwAGAAAAAADIPAIYAAAAAAAg8whgAAAAAACAzCOAAQAAAAAAMo8ABgAAAAAAyLz/AyhwEW8LzkGgAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(15,6))\n", "plt.subplot(121)\n", "plt.plot(np.arange(chain.shape[0]),chain)\n", "plt.title('Trace Plot for $\\\\mu$')\n", "\n", "plt.subplot(122)\n", "plt.hist(chain,orientation='horizontal',bins=30)\n", "plt.title('Histogram for $\\\\mu$')\n", "\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# How do we know this chain has converged to the posterior?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Standard Error of the Mean\n", "\n", "This investigates the question how does the **mean** of $\\theta$ deviate in our chain, and is capturing the *simulation error* of the mean rather than underlying uncertainty of our parameter $\\theta$:\n", "\n", "$$\n", "SE^{\\bar{\\theta}} = \\frac{\\text{Posterior Standard Deviation}}{\\sqrt{L}}\n", "$$\n", "\n", "where $L$ is the chain length (the number of iterations in your chain). Note that the package we'll be using calls this MC Error.\n", "\n", "For our problem, this is:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T07:57:53.992359", "start_time": "2016-03-02T07:57:53.988659" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Standard Error of the Mean: 0.011656241240510384\n" ] } ], "source": [ "print(\"Standard Error of the Mean: \", chain.std()/np.sqrt(chain.shape[0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is saying that very little of our posterior variation in $\\theta$ is due to sampling error (that is good). We can visualize this by examining the moving average of our chain as we move through the 5000 iterations:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T07:57:59.840736", "start_time": "2016-03-02T07:57:59.296811" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# pandas makes this easy:\n", "df_chain = pd.DataFrame(chain,columns=['theta'])\n", "df_chain['ma_theta'] = df_chain.theta.rolling(window=100,center=False).mean()\n", "#df_chain['ma_theta'] = pd.stats.moments.rolling_mean(df_chain.theta,100)\n", "df_chain['iteration'] = df_chain.index.values\n", "ax = df_chain.plot(x=['iteration'],y=['theta','ma_theta'],figsize=(15,7))\n", "ax.lines[-1].set_linewidth(4)\n", "ax.lines[-1].set_color('k')\n", "ax.lines[0].set_label(\"$\\\\theta$\")\n", "ax.lines[-1].set_label(\"Moving Average of $\\\\theta$\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a good sign that our chain is stable, since both the individual samples of $\\theta$ in our chain and the mean of the samples dance around a stable value of $\\theta$. The calculation above makes this more concrete. There are time series versions of this calculation that accounts for the fact that the chain is not iid." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Autocorrelation Plots" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T07:58:08.108839", "start_time": "2016-03-02T07:58:06.470913" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import pymc3 as pm3\n", "\n", "lags=np.arange(1,100)\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(lags, [pm3.autocorr(chain, l) for l in lags])\n", "_ = ax.set(xlabel='lag', ylabel='autocorrelation', ylim=(-.1, 1))\n", "plt.title('Autocorrelation Plot')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Acceptance Rate for the MH Algorithm\n", "\n", "Recall that we want the acceptance rate to be in the range .2 to .4. For our problem [this paper](http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aoap/1034625254) suggests an acceptance rate of .234 for random walk MH.\n", "\n", "Since the number of **new** members in the chain represent the number of acceptances, count changes in chain values and divide by total chain length to calculate acceptance rate:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T07:58:10.318014", "start_time": "2016-03-02T07:58:10.311158" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Acceptance Rate is: 0.4232\n" ] } ], "source": [ "changes = np.sum((chain[1:]!=chain[:-1]))\n", "print(\"Acceptance Rate is: \", changes/(chain.shape[0]-1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The acceptance rate is helpful in describing convergence because it indicates a good level of \"mixing\" over the parameter space. Here the acceptance rate is too low, so we should decrease proposal width and re-run our MH MCMC sampler.\n", "\n", "> Note: modern software (like pymc) can auto-tune $\\omega$ to achieve a desired acceptance rate." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Geweke Diagnostic\n", "\n", "We can explicitly think of this test as a test for the Ergodicity (stationarity) of your chain.\n", "\n", "Take the first 10 and last 50% of your chain and do a z test comparing means (correcting for autocorrelation). Software packages, take this a step further: The geweke function in pymc3 by default chooses the first 10% of your chain, and the final 50%; divides the final 50% of the chain into 20 segments and performs a z-test for each segment. You want to fail to reject the null, since the hypothesis is:\n", "\n", "$$\n", "H_0: \\theta_{10\\%} = \\theta^s_{50\\%} \\\\\n", "H_1: \\theta_{10\\%} \\ne \\theta^s_{50\\%} \n", "$$\n", "for each segment $s$. If our means are the same (we fail to reject the null), then we have strong evidence of chain convergence." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T07:58:17.886024", "start_time": "2016-03-02T07:58:17.570793" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gw_plot = pm3.geweke(chain)\n", "plt.scatter(gw_plot[:,0],gw_plot[:,1])\n", "plt.axhline(-1.98, c='r')\n", "plt.axhline(1.98, c='r')\n", "plt.ylim(-2.5,2.5)\n", "plt.title('Geweke Plot Comparing first 10% and Slices of the Last 50% of Chain')\n", "plt.xlim(-10,2510)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Even without dropping any burn-in observations, we have convergence. We only start seeing issues when we restrict ourselves to the first 5 values in the chain. Suggests we should drop the first few dozen observations for burn-in." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T07:58:24.195380", "start_time": "2016-03-02T07:58:23.859100" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gw_plot = pm3.geweke(chain,.001,.5,20)\n", "plt.scatter(gw_plot[:,0],gw_plot[:,1])\n", "plt.axhline(-1.98, c='r')\n", "plt.axhline(1.98, c='r')\n", "plt.ylim(-2.5,2.5)\n", "plt.xlim(-10,2510)\n", "plt.title('Geweke Plot Comparing first .1% and Slices of the Last 50% of Chain')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Gelman Rubin Diagnostic\n", "\n", "If our MH MCMC Chain reaches a stationary distribution, and we repeat the excercise multiple times, then we can examine if the posterior for each chain converges to the same place in the distribution of the parameter space.\n", "\n", "Steps:\n", "1. Run $M>1$ Chains of length $2 \\times N$.\n", "2. Discard the first $N$ draws of each chain, leaving $N$ iterations in the chain.\n", "3. Calculate the within and between chain variance.\n", " * Within chain variance:\n", " $$\n", " W = \\frac{1}{M}\\sum_{j=1}^M s_j^2 \n", "$$\n", " where $s_j^2$ is the variance of each chain (after throwing out the first $N$ draws).\n", " * Between chain variance:\n", " $$\n", " B = \\frac{N}{M-1} \\sum_{j=1}^M (\\bar{\\theta_j} - \\bar{\\bar{\\theta}})^2\n", "$$\n", " \n", " where $\\bar{\\bar{\\theta}}$ is the mean of each of the M means.\n", "4. Calculate the estimated variance of $\\theta$ as the weighted sum of between and within chain variance.\n", "$$\n", "\\hat{var}(\\theta) = \\left ( 1 - \\frac{1}{N}\\right ) W + \\frac{1}{N}B\n", "$$\n", "5. Calculate the potential scale reduction factor.\n", "$$\n", "\\hat{R} = \\sqrt{\\frac{\\hat{var}(\\theta)}{W}}\n", "$$\n", "\n", "We want this number to be close to 1. Why? This would indicate that the between chain variance is small. This makes sense, if between chain variance is small, that means both chains are mixing around the stationary distribution. Gelmen and Rubin show that when $\\hat{R}$ is greater than 1.1 or 1.2, we need longer burn-in.\n", "\n", "Let's run 2 chains:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T07:59:14.474005", "start_time": "2016-03-02T07:58:28.055943" } }, "outputs": [], "source": [ "chain1 = sampler(data,samples=5000,mu_init=9,sigma=sigma,proposal_width=2,\n", " mu_prior_mu=mu_prior,mu_prior_sd = sigma_prior)\n", "chain2 = sampler(data,samples=5000,mu_init=9,sigma=sigma,proposal_width=2,\n", " mu_prior_mu=mu_prior,mu_prior_sd = sigma_prior)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T07:59:44.103696", "start_time": "2016-03-02T07:59:43.638529" } }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(15,5))\n", "plt.plot(np.arange(5001),chain1)\n", "plt.plot(np.arange(5001),chain2,alpha=.7)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "ExecuteTime": { "end_time": "2016-03-02T07:59:46.241200", "start_time": "2016-03-02T07:59:46.219331" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Gelmen-Rubin Diagnostic: 1.161636365352385\n" ] } ], "source": [ "# note, I can't use pm3.gelmen_rubin() because my chains are not pymc trace objects :-(\n", "burn_in = 10\n", "length = 10\n", "\n", "n = chain1[burn_in:burn_in+length].shape[0]\n", "\n", "W = (chain1[burn_in:burn_in+length].std()**2 + chain2[burn_in:burn_in+length].std()**2)/2\n", "mean1 = chain1[burn_in:burn_in+length].mean()\n", "mean2 = chain2[burn_in:burn_in+length].mean()\n", "mean = (mean1 + mean2)/2\n", "B = n * ((mean1 - mean)**2 + (mean2 - mean)**2)\n", "var_theta = (1 - 1/n) * W + 1/n*B\n", "print(\"Gelmen-Rubin Diagnostic: \", np.sqrt(var_theta/W))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It should be evident that Gelmen-Rubin has two factors at play: burn-in and chain length. Really this criteria can be used ex-post to justify decisions on burn-in and chain length. " ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Univariate Approaches\n", "\n", "The diagnostics we have discussed are all univariate (they work perfectly when there is only 1 parameter to estimate). Other diagnostics have been derived for the multivariate case, but these are useful only when using Gibbs Samplers or other specialized versions of Metropolis-Hastings.\n", "\n", "So most people examine univariate diagnostics *for each variable*, examine autocorrelation plots, acceptance rates and try to argue chain convergence based on that- unless they are using Gibbs or other specialized samplers." ] } ], "metadata": { "hide_input": false, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.4" }, "latex_envs": { "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 0 } }, "nbformat": 4, "nbformat_minor": 1 }